Answers
The equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).
How to Write an Equation in Point-slope Form?An equation can be written in point-slope form, where m represents the slope and (a, b) represents a point on the line, as: y - b = m(x - a).
From the given information describing Bray's distance from home after some time, we have the following parameters:
x = hours (time)y = distance (miles)Slope (m) = -6A point = (1/2, 4)Substitute m = -6 and (a, b) = (1/2, 4) into y - b = m(x - a):
y - 4 = -6(x - 1/2)
Therefore, the equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).
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Related Questions
+
e. The ratio of walnuts to peanuts in a can of mixed nuts is 3 to 5. There are
walnuts, peanuts, and cashews in the mix. The mix has 100 nuts in total. If
there are 18 walnuts, use a proportion and additional math to determine how
many cashews there are.
$2
3
Answers
The number of cashews in the can are 52.
Here, we are given that the ratio of walnuts to peanuts in a can of mixed nuts is 3 to 5.
⇒ walnuts : peanuts = 3 : 5
The number of walnuts in the packet are = 18
⇒ 18 : peanuts = 3 : 5
18/ peanuts = 3/5
peanuts = (5/3) × 18
peanuts = 30
Now, we know that the total number of nuts = 100
⇒ cashews + walnuts + peanuts = 100
cashews + 18 + 30 = 100
cashews + 48 = 100
cashews = 100 - 48
cashews = 52
Thus, the number of cashews in the can are 52.
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Amelia has 120 ten-dollar bills and 75 twenty-dollar bills. What is the ratio of ten-dollar bills to twenty-dollar bills
Simplify your answer.
Enter your answer as a fraction.
●
please help
Answers
Answer:
24/15
Step-by-step explanation:
120 : 75 =
120/5 : 75/5 =
24 : 15 =
24/15
Answer:
8 : 5 or 8/5
Step-by-step explanation:
starts as 120 : 75
divide both by 5
= 24 : 15
divide both by 3
= 8 : 5 or 8/5
you just need to get them down to the smallest they can. in this case it is 8 and 5. for every 8 $10 bills there are, you have 5 $20 bills.
9x-9y-0
-3x+3y=0
elimination process
Answers
Answer:
(-10,-10)Step-by-step
explanation:
Yes 9x-9y=03x-4y=10In
elimination, we want both equations to have the same form and like terms to be lined up. We have that. We also need one of the columns with variables to contain opposites or same terms. Neither one of our columns with the variables contain this. We can do a multiplication to the second equation so that the first terms of each are either opposites or sames. It doesn't matter which. I like opposites because you just add the equations together. So I'm going to multiply the second equation by -3.I will rewrite the system with that manipulation:9x-9y=0-9x+12y=-30----------------------Add them up!0+3y=-30 3y=-30 y=-10So now once you find a variable, plug into either equation to find the other one.I'm going to use 9x-9y=0 where y=-10.So we are going to solve for x now.9x-9y=0 where y=-10.9x-9(-10)=0 where I plugged in -10 for y.9x+90=0 where I simplified -9(-10) as +90.9x =-90 where I subtracted 90 on both sides.x= -10 where I divided both sides by 9.The solution is (x,y)=(-10,-10)
Perform the operation and write the result in the standard form.
(1 + 9i)(1 - 9i)
Answers
Answer:
10-18i
Step-by-step explanation:
1(1-9i)+9(1-9i)
1-9i+9-9i
1+9-9i-9i
10-18i
Explanation:
(1+9i)(1-9i)
=(1-9i+9i-81i^2)
(Remember i^2 is -1)
=(1+81)
=82
In standard form, its written as 82+0i
Bill school is selling tickets to a fall musical. On thefirst day of ticket sales to school sold one adult ticket and 6 children tickets for a total of $52. The school took in $66 on the second day by selling 1 adult ticket and 8 child tickets. Find the price of an adult ticket
Answers
The price of an adult ticket is x= $10
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let the adult ticket be x
Let the children ticket be y
first day,
1*x + 6*y = 52
x + 6y = 52 equation 1
second day,
1*x + 8*y = 66
x + 8y = 66 equation 2
Solving both the equations
Subtracting equation 2 -equation 1, we get
x + 8y - x - 6y = 66 - 52
2y = 14
y = 7
putting the value of y in equation 1, we get
x + 6*7 = 52
x = 52 - 42
x = 10
Therefore, price of an adult ticket is x= $10
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the plane that is defined by a fixed z coordinate and contains the point(1,2,3)
Answers
The plane where the point is located and which has a fixed z coordinate (1,2,3) is y=2x.
Given that,
The plane where the point is located and which has a fixed z- coordinate (1,2,3).
The plane has the point (1, 2, 3) and the z-axis.
Any plane that has the z-axis is of the type that (0,0,1)
Therefore, By cross product of the two points we can find the equation.
Let take a matrix with x,y and z
We can se in the picture there is a matrix.
We now find the determination of that matrix .
determination means the scalar value calculated for a given square matrix is the determinant of a matrix. The determinant is a concept in linear algebra, and its components are square matrixes. It can be viewed as the matrix transformation's scaling factor. useful for performing calculus operations, computing the inverse of a matrix, and solving systems of linear equations.
-2x+y=0
y=2x
Therefore, The plane where the point is located and which has a fixed z coordinate (1,2,3) is y=2x.
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Suppose you want to have $600,000 for retirement in 30 years. Your account earns 6% interest. How much would you need to deposit in the account each month?
Answers
To have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.
As given in the question,
Final amount 'A'= $600,000
Time 't' = 30years
Rate of interest 'r'= 6%
Month =12
Let 'P' be the amount deposit in the account each month
[tex]A = \frac{(P(1+\frac{r}{m})^{mt}-1 )}{\frac{r}{m} }\\\\\implies 600,000 = \frac{(P(1+\frac{6}{12\times 100})^{12\times 30}-1 )}{\frac{6}{12\times 100} }\\\\\implies 600,000 \times \frac{1}{200}= P (\frac{12.06}{12})^{360}-1 \\\\\implies 3000 +1 = P(1.005)^{360} \\\\\implies P = \frac{3001}{6.02258} \\\\\implies P = \$498.29[/tex]
Therefore, to have $600,000 for retirement in 30 years with 6% interest , we need to deposit $498.29 in the account each month.
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If the graph of the parent function f(x) = x is 7 units up and stretched vertically by a factor of 3
Answers
The transformed function can be seen in the image below, and the rule is:
g(x)= x/3 + 7
How to get the transformed function?
Here we have the parent function, and we want to apply a translation of 7 units up and stretch it vertically by a scale factor of 3
First, we need to apply the translation, remember that a vertical translation of N units is written as:
g(x) = f(x) + N
If we want the translation to be upwards, then we need to use a positive value of N, so in this case we wil have:
g(x) = f(x) + 7
And now we apply a stretch of scale factor 3, this means that we need to divide the variable inside of the function by 3, so we get:
g(x) = f(x/3) + 7
This will give:
g(x)= x/3 + 7
Where we use the fact that f(x) = x
The graph of this function can be seen below.
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Find the intervals where f(x) is increasing or decreasing: √x -2x. Ans: increasing (0, 1/4) Decreasing (1/4, ∞)
Answers
Answer:
[tex]\textsf{Increasing function}: \quad \left[0, \dfrac{1}{16}\right)[/tex]
[tex]\textsf{Decreasing function}: \quad \left(\dfrac{1}{16}, \infty\right)[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\sqrt{x}-2x[/tex]
As a negative number cannot be square rooted, the domain of the function is restricted to [0, ∞).
[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]
Differentiating produces an algebraic expression for the gradient as a function of x. Therefore, differentiate the given function:
[tex]\begin{aligned}f(x) & = \sqrt{x}-2x\\& = x^{\frac{1}{2}}-2x\\\implies f'(x) & = \dfrac{1}{2}x^{\left(\frac{1}{2}-1\right)}-2x^{(1-1)}\\ & = \dfrac{1}{2}x^{-\frac{1}{2}}-2x^0\\ & = \dfrac{1}{2\sqrt{x}}-2\end{aligned}[/tex]
Increasing function
To find the interval where f(x) is increasing, set the differentiated function to more than zero and solve for x:
[tex]\begin{aligned}f'(x) & > 0\\\implies \dfrac{1}{2\sqrt{x}}-2 & > 0\\\dfrac{1}{2\sqrt{x}} & > 2\\\ \dfrac{1}{2} & > 2\sqrt{x}\\\dfrac{1}{2 \cdot 2} & > \sqrt{x}\\ \dfrac{1}{4} & > \sqrt{x}\\ \sqrt{x} & < \dfrac{1}{4}\\\left(\sqrt{x}\right)^2 & < \left(\dfrac{1}{4}\right)^2\\ x & < \dfrac{1}{16}\end{aligned}[/tex]
As the domain is restricted, the function is increasing when:
[tex]\textsf{Solution}: \quad 0 \leq x < \dfrac{1}{16}[/tex]
[tex]\textsf{Interval notation}: \quad \left[0, \dfrac{1}{16}\right)[/tex]
Decreasing function
To find the interval where f(x) is decreasing, set the differentiated function to less than zero and solve for x:
[tex]\begin{aligned}f'(x) & < 0\\\implies \dfrac{1}{2\sqrt{x}}-2 & < 0\\\dfrac{1}{2\sqrt{x}} & < 2\\\ \dfrac{1}{2} & < 2\sqrt{x}\\\dfrac{1}{2 \cdot 2} & < \sqrt{x}\\ \dfrac{1}{4} & < \sqrt{x}\\ \sqrt{x} & > \dfrac{1}{4}\\\left(\sqrt{x}\right)^2 & > \left(\dfrac{1}{4}\right)^2\\ x & > \dfrac{1}{16}\end{aligned}[/tex]
Therefore, the function is decreasing when:
[tex]\textsf{Solution}: \quad x > \dfrac{1}{16}[/tex]
[tex]\textsf{Interval notation}: \quad \left(\dfrac{1}{16}, \infty\right)[/tex]
Note: The answer quoted in the original question is incorrect for the quoted function (please refer to the attached graph for proof).
Differentiation Rules
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
The number of words in books are discrete or continuous
Answers
Graduation gift of $5,000 average 2.5% interest. 3. what will the total value be after 10 years simple interest?
Answers
5000 x 0.025 x 10
= 1250
Total value = 5000 + 1250
= 6250
Match the Statement with the property that matches. A. R=R B. 5-P C. If 3 = x and y = -2 Then the expression y = x + b can be written as -2 = 3 + b D. a=4 Then it can be said that a = b E. DEIR then DF = LR F. VW - WY - VT Substitution Property Transitive Property Symmetric Property Reflexive Property Segment Addition Postulate Segment Congruence Postulate
Answers
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. a) R=R is a reflexive property.
b) 5-P Substitution Property, c) If 3 = x and y = -2 Then the expression y = x + b can be written as -2 = 3 + b is a substitution property, d) a=4 Then it can be said that a = b e)DEIR then DF = LR Segment Addition Postulate
f)VW - WY - VT is a Transitive Property
What is Expression?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
We have match the given expression with an appropriate property.
a) R=R is a reflexive property.
b) 5-P Substitution Property
c) If 3 = x and y = -2 Then the expression y = x + b can be written as -2 = 3 + b is a substitution property
d) a=4 Then it can be said that a = b
e)DEIR then DF = LR Segment Addition Postulate
f)VW - WY - VT is a Transitive Property
Therefore .a) R=R is a reflexive property. b) 5-P Substitution Property, c) If 3 = x and y = -2 Then the expression y = x + b can be written as -2 = 3 + b is a substitution property, d) a=4 Then it can be said that a = b e)DEIR then DF = LR Segment Addition Postulate f)VW - WY - VT is a Transitive Property.
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f(x)=3x-3. find f(4)
Answers
Answer:
f(4)=9
Step-by-step explanation:
The given function is
F(x)=3x-3
so,
f(4)=3*4-3
f(4)=12-3
f(4)=9
putting 4 in place of x we get answer of the question.
Find the lateral area of this square based pyramid. base is 10 ft. and slant is 10 ft.
Answers
The lateral area of the square pyramid that has a base of 10ft and height of 10 ft is calculated as: 200 ft²
How to Determine the Lateral Surface Area of a Square Pyramid?A square pyramid is a solid that has a square base and four triangular lateral faces.
The lateral area of the square pyramid is therefore the total area of the four triangular lateral faces of the square pyramid.
Area of one triangular lateral face = 1/2(base)(height)
Lateral area of the square pyramid = Total area of the four triangular lateral faces = 4 × 1/2(base)(height) = 2(base)(height)
We know the following:
Base = 10 ft
Height = 10 ft
Therefore:
Lateral area of the square pyramid = 2(10)(10)
Lateral area of the square pyramid = 200 ft²
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Please help meeee!!!!
Answers
Answer:2
Step-by-step explanation: x+1+2x=3x+1 3x+1=7 3x=7-1 x=6/3 x=2
hope it helps
Answer:
3
Step-by-step explanation:
x+1+2x=7
variables should be on the left and the whole number on the right.
something like this: x+2x=7-1
simplify the equation: 3x=6
find x: x= 6/3=2
so u know x is 2
then substitute the 2 into x. so 2+1 =3#
Your answer is three.
Calculate the area of one triangle so that you can begin building the tabletop .What is the area of each triangle in square inches
Answers
A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
The area of each triangle is 200 square inches.
What is a right triangle?A triangle in which one of the interior angles is 90° is called a right triangle. The longest side opposite to the right angle is the hypotenuse and the two arms of the right angle are the height and the base.
We have,
The area of a right triangle is given by:
= 1/2 x base x height
We have from the figure,
Base = 20 inches
Height = 20 inches
Area = 1/2 x 20 x 20
Area = 10 x 20
Area = 200 square inches
Thus the area of each triangle is 200 square inches.
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The complete question is:
You work as an assistant to a carpenter who designed the tabletop below. He tells you that each shape is a right triangle, and each is the same size. You now need to calculate the area of one triangle so that you can begin building the tabletop. What is the area of each triangle in square inches?
A. 200 square inches
B. 400 square inches
C. 570 square inches
D. 2,800 square inches
E. 5,600 square inches
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the following equation algebraically. Show your work.
17=−13−8x
Answers
Answer:
-15/4 = x
Step-by-step explanation:
17 = -13 -8x
Solving for x
Add 13 to each side
17 +13 = -13+13-8x
30 = -8x
Divide each side by -8
30/-8 = -8x/-8
Simplify by dividing the top and bottom by 2
-15/4 = x
compare -3/4 and -5/16
A. -3/4 < -5/16
B. -3/4 > -5/16
C. -3/4 = -5/16
Answers
LCM can help us to compare the two of the given fractions. The correct option is A, -(3/4) < -(5/16).
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
Bring both the terms to the same denominator for easy comparison. Now, since the LCM of 4 and 16 is 16. Therefore, we can write the two of the fractions as,
-(3/4) = -(3×4)/(4×4) = -12/16
-(5/16) = -5/16
Further, we can write the comparison of the two fractions as,
-12/16 < -5/16
-(3/4) < -(5/16)
Hence, the correct option is A, -(3/4) < -(5/16).
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How much will a person pay for 6.7 pounds of bananas at a price of $0.64 per pound?
Answers
Answer:
Price per pound = $0.64
which means one pound of banana costs 0.64$.
so,If 1 pound costs 0.64$ then 6.7 pounds would cost:
1 pound = $0.64
6.7 pounds= 0.64× 6.7
that is equal to $4.288.
Step-by-step explanation:
Price per pound = $0.64
which means one pound of banana costs 0.64$.
so,If 1 pound costs 0.64$ then 6.7 pounds would cost:
1 pound = $0.64
6.7 pounds= 0.64× 6.7
that is equal to $4.288.
What is 0.0001 as a
single digit times a
power of 10.
Answers
Answer:
[tex]10^{-4}[/tex]
Step-by-step explanation:
0.0001
1/10,000
1/[tex]10^{4}[/tex]
[tex]10^{-4}[/tex]
Aubrey worked at three part-time jobs last week. At one job, she worked 15 hours at a salary of S15 per hour, at another she worked 10 hours at S14 per hour,
and at the third she worked 11 hours at $21 per hour. What was her mean hourly wage?
Answers
A storage locker measures 8 feet wide,
12 feet deep, and 9 feet high. The
monthly rental price for the locker
is $3.60 per cubic yard. How much
does it cost to rent the locker each
month? Explain.
Answers
Then the rent is
($3.60/yd³) × (8/3 yd) × (4 yd) × (3 yd) = $115.20
The rental cost each month is $115.20.
Which transformation would take Figure A to Figure B?
Answers
Answer:
Reflection over y- axis
7th grade question
2. Mateo is draining a pool at a rate of 1/8 of a gallon of water every 1/2 hour.
If he continues to drain the pool at this rate, how much water will be
drained in 1 hour?
A.4 gallons
B.1 gallon
C. 1/2 gallon
D.1/4 gallon
Answers
Answer:
1/4 gallon
Step-by-step explanation:
Just multiply the numerator and denominator of the given rate by 2:
2(1/8) gallon 1/4 gallon
------------------ = ---------------- = 1/4 per gallon
2(1/2) hour 1 hour
If anyone can help me with this I'd appreciate it a ton!
Thank you so much.
Answers
Answer:
help this yuo what is yuor problem
Ellen wanted to buy the following items: A DVD player for $49.95 A DVD holder for $19.95 Personal stereo for $21.95. Does Ellen have enough money to buy all three items if she has $90?
Answers
Answer: no she dosen't
Step-by-step explanation:
If you were to add up all three numbers
49.95+19.95+21.95=91.85
Which means she is $1.85 short to buy all of the items
28:32 simplified
Does any one know?
Answers
it will be 7:8
Step-by-step explanation:
28/4 32/4
7 8
Name three points that are collinear
Answers
Answer:
B, J, C.
Collinear points means the points are on the same straight line, which means they have the same gradient. B, J, C are the only points on the sane straight line.
The sun of 2,5, and a number amounts to 14. Find the number
Answers
Answer:
x=is the number searched
we have to solve this equation:
(2/5)x=14
x=14*5/2=35
35
Step-by-step explanation:
The answer would be 7.
This can be represented as ,
:2+5+x =14
:7+x=14
:x=14-7
:x= 7
Answer this question please
Answers
The inequality for 2/3 I 4v + 6 I - 2 ≤ 10 is -6≤v≤3.
Given the inequality is 2/3 I 4v + 6 I - 2 ≤ 10
Isolate the variable by dividing each side by factors that don't contain the variable.
2/3 I 4v + 6 I ≤ 10 +2
arrange the constants on the right side.
2/3 I4v + 6I ≤ 12
multiply the terms.
8v + 12/3 ≤ 12 or -8v - 12/3 ≤ 12
8v + 12 ≤ 36 or -8v -12 ≤ 36
8v ≤ 36 -12 or -8v ≤ 36 + 12
8v ≤ 24 or -8v ≤ 48
v ≤ 24/8 or v ≤ 48/8
v ≤ 3 or v≥-6
therefore, -6 ≤ v ≤ 3.
Hence the inequality is -6 ≤ v ≤ 3.
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