Final answer:
Mrs. Smith will donate $20 for Sam walking 20 miles, illustrating a direct proportional relationship with a constant of proportionality of $1 per mile, which is a simple yet effective example of how constants of proportionality function in everyday scenarios.
Explanation:
In the fundraiser mentioned, Mrs. Smith pledges $1 for each mile walked. If Sam walks 20 miles, Mrs. Smith will donate $20. The constant of proportionality in this problem is $1 per mile.
You can see this relationship as a simple formula: total donation = $1 × number of miles walked. So, if we replace "number of miles walked" with 20, the formula would be total donation = $1 × 20 = $20. This illustrates how the initial pledge creates a directly proportional relationship between the money donated and the miles walked.
The constant of proportionality here is crucial because it tells us how much money will be donated per mile that Sam walks. It is a straightforward example of how constants of proportionality work in real-life scenarios, similar to being paid for each call made in a phone drive or being charged per hour of tutoring.
Koby's solution for 4(x - 3) = x + 2 is shown at the
right. Did he solve the equation correctly? Explain why
or why not.
4(x - 3) = 3x +2
4x - 12 = 1/x + 2
2. (4X – 12) = 2 · ( 3x + 2
8x - 12 = x + 2
8x = x + 14
7x = 14
x
=2
Koby did not solve the equation correctly. The correct solution for 4(x - 3) = x + 2 is x = 14/3 or approximately 4.667. The steps include distribution, combining like terms, and isolating the variable.
The student's solution contains errors in the algebraic process. The correct steps to solve the original equation 4(x - 3) = x + 2 are as follows:
Distribute the 4 into the parentheses: 4x - 12 = x + 2.
Subtract x from both sides to get all the x terms on one side: 4x - x - 12 = 2.
Simplify the equation: 3x - 12 = 2.
Add 12 to both sides to isolate the variable term: 3x = 14.
Divide both sides by 3 to solve for x: x = 14/3.
The correct solution is x = 14/3 or approximately 4.667, not x = 2 as Koby had. To check the solution, you substitute the value back into the original equation:
4(14/3 - 3) = 14/3 + 2
which simplifies to:
56/3 - 12 = 14/3 + 2
and further to:
56/3 - 36/3 = 14/3 + 6/3
resulting in an identity:
20/3 = 20/3.
is y-4=2(x-2) and 4x-2y=5 perpendicular
Answer:
Therefore,
Slopes are Equal, Hence the Lines are not Perpendicular.
Step-by-step explanation:
Given:
[tex]y-4=2(x-2)=2x=-4\\\\y=2x[/tex] .......Equation ( 1 )
[tex]4x-2y=5\\2y=4x-5\\\\y=2x-\dfrac{5}{2}[/tex] .......Equation ( 2 )
Comparing with,
[tex]y=mx+c[/tex] ......General Slope point form
Where m =slope
We get
[tex]Slope = m1 = 2[/tex] For Equation ( 1 )
[tex]Slope = m2 = 2[/tex] For Equation ( 2 )
Hence,
[tex]m1=m2[=2[/tex]
Therefore, Slopes are Equal Hence the Lines are Parallel not Perpendicular.
For Perpendicular we require
[tex]m1\times m2=-1[/tex]
Therefore,
Slopes are Equal, Hence the Lines are not Perpendicular.
Which term completes the product so that it is the difference of squares?
| (-5x-3)(-5x+_
.
..
со со
Answer:
3
(-5x - 3)(-5x + 3)
Step-by-step explanation:
Difference of squares is a special type of factoring when you are subtracting two numbers that are perfect squares. Perfect squares are numbers that, when you find its square root, it is a whole number.
Difference of squares follows this rule:
a² - b² = (√a² - √b²)(√a² + √b²) = (a - b)(a + b)
Notice in the factored form, you take the same number in both brackets. In one set of brackets you add the numbers. In the other brackets, you subtract the numbers.
In (-5x - 3)(-5x + __), the blank in the second bracket will use the same number as the second number in the first brackets.
(-5x - 3)(-5x + 3)
evaluate the expression 3(x-1)2nd power +2x-7 for x=3
What is the first step for evaluating this expression?
Substitute 3 for X
distribute the 3
combine like terms
Answer:
11
3Step-by-step explanation:
Given
3(x - 1)² + 2x - 7 ← substitute x = 3 into the expression
= 3(3 - 1)² + 2(3) - 7
= 3(2)² + 6 - 7
= 3(4) - 1
= 12 - 1
= 11
The first step in evaluating the expression is to substitute 3 for x.
The first step in evaluating the expression 3(x-1)^2 + 2x - 7 for x=3 is to substitute 3 for x. This is because before you can simplify or combine like terms, you need to know the value of the variables involved. Once substitution is done, you can proceed with further simplification such as distributing and combining like terms.
A musicians hair was originally 11 2/3 inches long. She asked her hair dresser to cut off 5/8 of it off. How many inches did she have cut off?
Answer:
Step-by-step explanation:87
87
9. Abby walked 3 km west. Then she walked
twice as far going east. She continued east
for another kilometre, stopping 2 km east
of Lauren's home. When Abby started
walking, how far was she from Lauren's
home? Explain how you know.
Answer:
2km
Step-by-step explanation:
- Abby walked 3 km west: Abby is 3km west from her starting point.
- Then she walked twice as far going east: she walks 6km east so she's 3 km east from her starting point
- She continued east for another kilometre: She's is 4 km east from her starting point
- Stopping 2 km east of Lauren's home: She's currently 2 km east from Lauren's home and 4km east from her starting point. Therefore, Abby's starting point is 4km - 2km = 2km west from Lauren's home
what is the product of r^2 -3 and 2r
Answer:
- 6r³.
Step-by-step explanation:
Here, we have to find the product of r², - 3 and 2r.
Now, the product is, P = (r²)(- 3)(2r)
⇒ [tex]P = (- 3) \times (2) \times r^{2}\times r[/tex]
{Seperating each terms as the terms are in product form}
⇒ [tex]P = - 6 \times r^{2 + 1}[/tex]
{Using the property of exponent that [tex]x^{a}\times x^{b} = x^{a + b}[/tex]}
⇒ P = - 6r³ (Answer)
Which expression means 9.7 split into a certain number of equal parts?
9.7n
9.7 + n
9.7 minus n
StartFraction 9.7 over n EndFraction
Answer:
Option D
Step-by-step explanation:
Just took the quiz :)
Answer:
it is the last answer
Step-by-step explanation:
2) The two rectangles shown are similar.
24 cm
9 cm
16 cm
What is the missing measurement?
Fx = 3 cm
G
x = 6 cm
H
x = 18 cm
J
x = 32 cm
Answer:
[tex]6\ cm[/tex]
Step-by-step explanation:
First Rectangle:
[tex]length(l_1)=24\ cm\\\\Width(b_1)=9\ cm[/tex]
Second Rectangle:
[tex]length(l_2)=16\ cm\\\\Let\ Width=b_2\ cm[/tex]
[tex]Since\ these\ two\ rectangles\ are\ similar\\\\\frac{l_2}{l_1}=\frac{b_2}{b_1}\\\\\frac{16}{24}=\frac{b_2}{9}\\\\16\times 9=24\times b_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cross\ multiplication\\\\b_2=\frac{16\times 9}{24}\\\\b_2=6\ cm[/tex]
What is the approximate value of ? Round your answer to the nearest hundredth. 1.25 3.00 3.75 4.25
Option C:
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]
Solution:
Given expression:
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]
Summation means sum of the numbers.
Put n = 1 to 5 and sum all the numbers.
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]
[tex]=3(0.2)^{1-1}+3(0.2)^{2-1}+3(0.2)^{3-1}+3(0.2)^{4-1}+3(0.2)^{5-1}[/tex]
[tex]=3(0.2)^{0}+3(0.2)^{1}+3(0.2)^{2}+3(0.2)^{3}+3(0.2)^{4}[/tex]
Using exponential rule: [tex]a^0=1[/tex], so that [tex]0.2^0=1[/tex]
[tex]=3(1)+0.6+0.12+0.024+0.0048[/tex]
[tex]=3.7488[/tex]
= 3.75
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]
Option C is the correct answer.
Hence approximate value of [tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex] is 3.75.
Answer:
C
Step-by-step explanation:
edge
50 + 50 - 25 x 0 +2 + 2
Answer:
104
Step-by-step explanation:
Any expression multiplied by 0 equals 0
when adding or subtracting 0, the quantity doesn't change
Answer:
I think it is 4 or 104. There are 2 ways to look at it.
Way #1:
50 + 50 = 100
100 - 25 = 75
75 x 0 = 0
2 + 2 = 4
0 + 4 = 4
Way #2:
50 + 50 = 100
25 x 0 = 0
100 - 0= 100
2 + 2 = 4
100 + 4 = 104
An angle with a measure of 36(degrees)would be classified as which type of angle?
Answer:
An acute Angle
Step-by-step explanation:
Any Angle that is from 1 to 89 degrees is considered an acute Angle.
Select the correct answer.
AB and BC form a right angle at point B. If A= (-3,-1) and B = (4,4), what is the equation of
O A.
x + 3y = 16
B. 2x + y = 12
C.-7x- 5y = -48
D. 7x - 5y = 48
Answer:
C. -7x- 5y = -48
Step-by-step explanation:
The vector AB is ...
AB = B -A = (4, 4) -(-3, -1) = (4+3, 4+1) = (7, 5)
The dot-product of this vector and the one in the direction of the line through B will be 0:
(7, 5)·(x -4, y -4) = 0
7(x -4) +5(y -4) = 0
7x +5y -48 = 0
Multiplying by -1 gives the form we see in answer choice C:
-7x -5y = -48
jamie has 8/10 of a candy bar leftover he want to split into 1/3 pieces how many 1/3 pieces can he make
Answer:
Step-by-step explanation: solution.. 8/10 of candy bar left over to be split into 1/3 pieces...
(8/10)÷1/3=12/5=2.4pieces
Can anyone help me with theses problems?
Which relationship describes angles 1 and 2?
Select each correct answer.
supplementary angles
adjacent angles
vertical angles
complementary angles
Answer:
it's supplementary angles
Step-by-step explanation:
1 + 2 =180
Plzzzzzzzzzzzzzzzzzzzzzzzzzzzz help will give brainliest:):):)
Answer:
Step-by-step explanation:
diameter of plate=30+5=35 cm
circumference of cake board=2π r=π d=35 d cm
Answer:
35π cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = πd ← d is the diameter
Here the diameter = 30 + 5 = 35 cm, thus
C = 35π cm
Is 24/40 4/5 a true proportion?
Answer:
no
Step-by-step explanation:
24 x 5 = 120
40 x 4= 160
How much simple interest will be charged on a 40,000 loan with a 7% interest rate that is paid back in 4 years?
Answer:$11200
Step-by-step explanation:
I = prt
I = 40,000( .07)(4)
I = $11200
What is 3 divided by 1773
The answer is 591 to the problem.
how do you solve a quadratic function using x^2+bx+c?
Answer:
Check the attachment, then plug in values as needed
Step-by-step explanation:
write an algebraic expression for the following: the product of 5 and the sum of 9 and y. if y = 3 what’s the value of the expression
Answer:
60
Step-by-step explanation:
5 x (9 + y)
= 5 x ( 9 + 3)
= 5 x (12)
=60
Final answer:
The algebraic expression is 5(9 + y), which becomes 5(12) when y equals 3, resulting in a value of 60.
Explanation:
The algebraic expression for the product of 5 and the sum of 9 and y is 5(9 + y). To find the value of this expression when y equals 3, you substitute 3 for y in the expression, getting 5(9 + 3). Following the order of operations, calculate the sum inside the parentheses first, which gives you 5(12), and then multiply by 5 to find the product, resulting in a final value of 60.
Write an equation for the nth term of the geometric sequences. Then Find a6
A. 2, 8, 32, 128, ...
B. 0.6, -3, 15, -75, ...
C. -1/8, -1/4, -1/2, -1, ...
D. 0.1, 0.9, 8.1, 72.9, ...
Answer: The nth term of a geometric progression is Tn = ar^(n-1)
A. 12
B. 3.6
C. -3/4
D. 0.6
Step-by-step explanation:
The nth term of a geometric progression is Tn = ar^(n-1)
Where Tn= nth term
a = first term
r = common ratio
n = number
A. a6 = (2*6) = 12
B. a6 = (0.6*6) = 3.6
C. a6 = (-1/8*6) = -3/4
D. a6 = (0.1*6) = 0.6
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Find the sum of a finite geometric series.
Amanda teaches the art of quilling to 4 students. These students each teach the art of quilling to 4 other students. If this process continues for 5 generations after Amanda,
people other than Amanda will know the art of quilling.
Answer:
4096
Step-by-step explanation:
4*4=16
16*4=64
64*4=256
256*4=1024
1024*4=4096
if this doesn't work, try the other products
Answer:
1,024
Step-by-step explanation:
Five generations after Amanda.
So, Amanda would be considered generation 0.
1st Generation- 4^1=4
2nd Generation-4×4=16
3rd Generation-16×4=64
4th Generation-64x4=256
5th Generation-256×4=1,024
What is the answer
9:3 :: 49 :
To solve this ratio problem, we need to determine the relationship between the given numbers and apply it to find the answer.
Explanation:The given expression is:
9:3 :: 49 :
To solve this, we need to determine the relationship between 9 and 3, and then apply the same relationship to 49.
The symbol '::' represents the ratio or proportion between the numbers before and after it.
9 divided by 3 is equal to 3, so the relationship here is that the first number is three times the second number.
Now, let's apply the same relationship to 49:
49 divided by 3 is equal to 16.33, so we can say that the answer is 16.33.
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The final answer is 9 : 3 :: 49 : 16.33.
Here's a step-by-step solution:
We need to find the missing number such that the ratios are equivalent. This can be written as a proportion: 9/3 = 49/x.First, simplify the left side: 9/3 = 3.So, we have: 3 = 49/x.Next, solve for x by multiplying both sides by x: 3x = 49.Finally, divide both sides by 3 to isolate x: x = 49/3.Therefore, x = 16.33 (rounded to two decimal places).The answer to the question is therefore 49 : 16.33.
The exterior angles of triangle UVW are ∠X, ∠Y, and ∠Z, and they are adjacent to ∠U, ∠V, and ∠W, respectively.
If m∠U is 33°, and m∠Z is 130°, what is m∠V?
Answer:
the answer is 97, I'll explain in the comments in a bit
^^
guy above me its right
What is the factored form of 3x + 21x-24?
Answer:
factorize form of the equation is [tex]24(x-1)=0[/tex] , where [tex]x=1[/tex]
Step-by-step explanation:
Given Equation:
[tex]3x + 21x-24=0[/tex]
Adding the terms of 'x' and taking constants on the other side.
[tex]24x-24=0[/tex]
The sign of the constant will change on changing the side of it.
[tex]24x=24[/tex]
[tex]x=\frac{24}{24}[/tex]
[tex]x=1[/tex]
So, the value of 'x' is 1
The factorized form of the equation can be made by taking the common value from the equation i.e
[tex]24x-24=0\\[/tex]
[tex]24(x-1)=0[/tex]
The diagram shows a sketch of John's yard. He wants to plant grass, so he must calculate the area of the yard. The distance from A to B is 200 feet; the distance from C to D is 260 feet, and the straight line distance between AB and DC is 220 feet. The area of the yard is
A) 5,720,000 square feet
B) 25,300 square feet
C) 50,600 square feet
D) 57,200 square feet
The area of the yard is 50,600 square feet.
Option: C.
Step-by-step explanation:
The given information forms a trapezoid.
The AB is the upper base (a) and its length is 200 feet.
The CD is the lower base (b) and its length is 260 feet.
A straight line distance from AB and CD is the height (h) and its measures as 220 feet.
The area of trapezoid A= [tex]\frac{a+b}{2} (h)[/tex].
A= [tex]\frac{200+260}{2} (220)[/tex].
=[tex]\frac{460}{2}(220)[/tex].
=230(220).
=50600 [tex]ft^2.[/tex]
Thus the area of John's yard is 50,600 square feet.
Melissa sells her art online for $49.50 per print. How many prints must she sell next month if she wants to earn at least $2000?
Answer:
41
Step-by-step explanation:
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. 40 prints must she sell next month if she wants to earn at least $2000
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
Melissa sells her art online for $49.50 per print.
We need to find how many prints she has to sell to earn atleast $2000.
Let us consider x be the number of prints.
Let us form proportional equation
Forty nine point five zero by one equal tp two thousand by x.
49.50/1=2000/x
Apply cross multiplication
49.50x=2000
Forty nine point five zero times of x equal to two thousand.
Divide both sides by 49.50
x=40.40
Hence 40 prints must she sell next month if she wants to earn at least $2000
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Layla is walking in a rectangular park. She walks one side that is 50 yards and then the other
side that is 120 yards. Layla develops a cramp in her leg and walks diagonally through the park
to head back home. What is the total distance that layla walked? (HINT: Final answer is
perimeter of the triangle park)
120 yd.
PARK
PARK
50 vd
Oak St
1
Park Rd
Total distance walked by Layla is 300 yards
Solution:
Given that,
Layla is walking in a rectangular park
She walks one side that is 50 yards and then the other side that is 120 yards
Length = 120 yards
Width = 50 yards
Layla develops a cramp in her leg and walks diagonally through the park to head back home
Let us find the length of diagonal of rectangle
[tex]d=\sqrt{w^2+l^2}[/tex]
[tex]d = \sqrt{50^2+120^2}\\\\d = \sqrt{2500+14400}\\\\d = \sqrt{16900}\\\\d = 130[/tex]
Thus length of diagonal is 130 yards
What is the total distance that layla walked?
Given that Final answer is perimeter of the triangle park
The diagonal and length and width forms a right angle triangle
Perimeter of triangle = diagonal length + width + length
Perimeter of triangle = 130 + 50 + 120 = 300
Thus total distance walked by Layla is 300 yards
The total distance Layla walked, including the two sides of the park and the diagonal path, is calculated using the Pythagorean theorem to be 300 yards.
Explanation:The question asks us to find the total distance Layla walked while going through the rectangular park diagonally. Layla first walks one side of the park which is 50 yards long and then the adjoining side which is 120 yards long. To do this, we will first find the length of the diagonal using the Pythagorean theorem and then add it to the sum of the two sides she walked to get the total distance. The Pythagorean theorem states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c2 = a2 + b2.
Applying the Pythagorean theorem to find the diagonal (hypotenuse):
Let a = 50 yards (length of the first side)Let b = 120 yards (length of the second side)c2 = a2 + b2 = 502 + 1202c2 = 2500 + 14400c2 = 16900c = √16900 = 130 yards (length of the diagonal)Now, we can find the total distance Layla walked:
Distance along the first side = 50 yardsDistance along the second side = 120 yardsDistance diagonally across the park = 130 yardsTotal distance = 50 yards + 120 yards + 130 yardsTotal distance = 300 yardsTherefore, the total distance Layla walked is 300 yards.
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