The range of values for the width w of the garden is 17 ≤ w ≤ 30.
Step-by-step explanation:
Given,
The length of the garden = 11 feet.
The perimeter of the garden = 56 feet (at least is the minimum value)
The perimeter of the garden = 82 feet (not more than is the maximum value)
step 1 :
Perimeter of a rectangle = 2 (length + width)
⇒ 56 = 2 (11 + width)
⇒ 56 = 22 + 2 width
⇒ 34 = 2 width
⇒ width = 34/2
∴ width = 17 feet
step 2 :
Perimeter of a rectangle = 2 (length + width)
⇒ 82 = 2 (11 + width)
⇒ 82 = 22 + 2 width
⇒ 60 = 2 width
⇒ width = 60/2
∴ width = 30 feet
step 3 :
The range of values for width 'w' is 17 ≤ w ≤ 30.
Answer:
[17,30]
Step-by-step explanation:
The base of an isosceles triangle is 7 units.
What could the length of the other sides be?
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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The frog is climbing out of a well that is 50 Feet deep. The frog can climb 7 feet per hour but then a rest for an hour and it slips back 3 feet while resting. How long will it take for the frog to get out of the well?
7-3=4 feet per hour
50 : 4 = 12,5 hour
The time taken by frog to get out of the well will be equal to [tex]22\frac{6}{7}[/tex] hours.
It is given that a well has a depth of 50 feet and a frog can climb 7 feet/hour but then takes a rest of 1 hour and slips by 3 feet.
We have to find out what time will it take for frog to get out of the well ?
What is the unitary method?
The unitary method is a method in which we find the value of a unit and then the value of the required number of units.
As per the question ;
The frog starts from the bottom of the well.
It is given that the well has a depth of 50 feet.
Frog can climb 7 feet/hour but then takes a rest of 1 hour and slips by 3 feet.
Let's check distance covered by frog in 2 hours ;
1st hour = 7 feet
2nd hour = 7 - 3 = 4 feet
So ,
In 2 hours frog covers a distance of 4 feet.
Hence ,
To climb 44 feet or 4 × 11 feet , the frog will take 2 × 11 or 22 hours
and
To climb rest of 6 feet distance , the frog would take [tex]\frac{6}{7}[/tex] of an hour.
Also ;
It is needed to be mentioned that once the frog reaches at the top of well it won't slip back.
So ,
The total time taken by frog to climb 50 feet deep well will be ;
= [tex]22\frac{6}{7}[/tex] hours
Thus , the time taken by frog to get out of the well will be equal to [tex]22\frac{6}{7}[/tex] hours.
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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?
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
What is the slope Intercept form of 8x-2y=-72
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.
Which matrix represents A-B.
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
36 cups equal how many ounces
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
To qualify for a store discount, Clay’s soccer team must spend at least $560 for new jerseys
Answer:
Step-by-step explanation: they must spend a minimum of $28 per jersey
What is the answer to this inequality -45x+12<112?
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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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?
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.
4/6 is less than or greater than 4/2
Answer:
No.
Step-by-step explanation:
4/6 as a decimal is 0.667 whereas 4/2 as a decimal is 2.
;D
counting back from 5 what number follow 4
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.
Does -2 4/5 + 6 1/3= 2/5
Answer:
yes.
Step-by-step explanation:
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
Answer:
a. a side length is (a+8)
b. a=9. (9+8)= 17
17×4= 68 is the perimeter
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
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”.
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°
3)
Which numerical expression equals − 1?
A) − 1(1− 1)
B) − (− 1)(− 1)
C) (− 1) + 1 − 1 (− 1)
D) − (− 1) − (− 1)(− 1)
Answer:
the correct answer is B
Answer: b
i just wrote it down on paper and used a calculator to reassure.
Factor the expression:
30 + 100c
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?
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?
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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Plz answer!! ASAP!!
(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°
(9-7i)–(4i +15)
What’s the answer
Answer:
-6 - 11i.
Step-by-step explanation:
(9-7i)–(4i +15)
= 9 - 7i - 4i - 15 Add like terms:
= -6 - 11i.
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
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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Use angle relationships and the diagram at right to write and solve an equation for 4x-5 2x+9
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
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.
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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15 times 18 + 12 divided by 3 +9
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]
If 10% of 60 is 6, what is 5% of 60?
Explain how you found your answer
Answer:
10% of 60 means (10 X 60)/100 so the answer is 6. Similarly 5% of 60 means (5 X 60)/100 , So the Answer is 3.
Step-by-step explanation:
Answer:
Step-by-step explanation:
If the function m not-equals 0 has an inverse function, which statement must be true?
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:
y=2x-5
write in y=mx+b form
3. What value of y makes this true?
25 - y<15
A. 8
B. 9
C. 10
D. 11
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
The slope of (3,6) and (5,2)
[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]