Answer:
m = [tex]\frac{y-6}{x}[/tex]
Step-by-step explanation:
Given
y = mx + 6 ( subtract 6 from both sides )
y - 6 = mx ( divide both sides by x )
[tex]\frac{y-6}{x}[/tex] = m
Please answer this correctly without making mistakes
Answer:
105/4 or 26.25 mi
Step-by-step explanation:
hillsdale to fairfax 8 7/8 = 71/8
fairfax to yardley = 17 3/8 = 139/8
71/8 + 139/8 = 105/4 or 26 2/8
Michael records the height of 1000 people. This data is a normal distribution and the sample mean was 0.75. Identify the margin of error for this data set.
Answer:
0.0284Step-by-step explanation:
The formula for calculating the Margin of error of a dataset is expressed as;
Margin of error = [tex]Z*\sqrt{\frac{p(1-p)}{n} } \\\\[/tex] where;
Z is the z-score of 95% confidence interval = 1.96
p is the sample proportion/mean = 0.75
n is the sample size = total number of people = 1000
Note that when the confidence interval is not given, it is always safe to use 95% confidence.
Substituting this values into the formula we have;
[tex]ME = 1.96*\sqrt{\frac{0.7(1-0.7)}{1000} } \\\\ME = 1.96*\sqrt{\frac{0.7(0.3)}{1000} } \\\\ME = 1.96*\sqrt{0.00021} } \\\\ME = 1.96*0.01449\\\\ME = 0.0284[/tex]
Hence the margin error for the dataset is 0.0284
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n
Answer: [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Step-by-step explanation:
[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3). What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8
Answer:
x + 2y = 8.
Step-by-step explanation:
Line goes through (-4, 0) and (4, -4).
The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.
Since we are looking for the equation of the line parallel to that line, the slope will be the same.
We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.
3 = (-1/2) * 2 + b
b - 1 = 3
b = 4.
So, we have y = -1/2x + 4.
1/2x + y = 4
x + 2y = 8.
Hope this helps!
ANSWEAr
x + 2y = 8
because it is
Which is the solution to the inequality?
2 3/5 <b-8/15
Answer:
3 2/15 <b
Step-by-step explanation:
2 3/5 <b-8/15
Add 8/ 15 to each side
2 3/5 + 8/ 15 <b-8/15 + 8/15
2 3/5 + 8 /15 <b
Get a common denominator
2 3/5 *3/3 + 8/15
2 9/15 + 8/15 < b
2 17/15 < b
2 + 15/15 + 2 /15 < b
3 2/15 <b
Answer:
B > 3 2/15
Step-by-step explanation:
I need some help with simplifying expressions, please. 8y - 9y =
As your first step to this problem, change the minus sign to plus a negative.
So we have 8y + -9y.
8y + -9y simplifies to -1y which is our final answer.
Note that if you wrote -y instead, it means the same thing.
However, use the 1 to help avoid confusion if you need it.
Factor.
x2 – 5x - 36
(x - 9)(x + 4)
(x - 12)(x + 3)
(x + 9)(x - 4)
(x + 12)(x - 3)
Answer:
The answer is option AStep-by-step explanation:
x² - 5x - 36
To factor the expression rewrite -5x as a difference
That's
x² + 4x - 9x - 36
Factor out x from the expression
x( x + 4) - 9x - 36
Factor out -9 from the expression
x( x + 4) - 9( x+ 4)
Factor out x + 4 from the expression
The final answer is
( x - 9)( x + 4)Hope this helps you
Answer:
[tex] \boxed{(x - 9) \: (x + 4) }[/tex]
Option A is the correct option.-
Step-by-step explanation:
( See the attached picture )
Hope I helped!
Best regards!
find the dimension of the swimming pool if the sum must be 50 feet and the length must be 3 times the depth.
Answer:
depth 5 8.3 ft, length 5 24.9 ft, width 5 16.8 ft
Solve systems of equations 15 points NOT CLICKBAIT!!! -6y+11y= -36 -4y+7x= -24
Answer:
x = -264/35
y = -36/5
Step-by-step explanation:
-6y + 11y = -36
-4y + 7x = -24
Solve for y in the first equation.
-6y + 11y = -36
Combine like terms.
5y = -36
Divide both sides by 5.
y = -36/5
Plug y as -36/5 in the second equation and solve for x.
-4(-36/5) + 7x = -24
Expand brackets.
144/5 + 7x = -24
Subtract 144/5 from both sides.
7x = -264/5
Divide both sides by 7.
x = -264/35
Answer: -264/35
Step-by-step explanation:
i did my work on a calculator
1. Transform the polar equation to a Cartesian (rectangular) equation: 2. Transform the Cartesian (rectangular) equation to a polar equation: y^2 = 4x
Answer:
Attachment 1 : 5x + 6y = 5, Attachment 2 : 4cotθcscθ
Step-by-step explanation:
Remember that we have three key points in solving these types of problems,
• x = r cos(θ)
• y = r sin(θ)
• x² + y² = r²
a ) For this first problem we need not apply the third equation.
( Multiply either side by 5 cos(θ) + 6 sin(θ) )
r [tex]*[/tex] ( 5 cos(θ) + 6 sin(θ) ) = 5,
( Distribute r )
5r cos(θ) + 6r sin(θ) = 5
( Substitute )
5x + 6y = 5 - the correct solution is option c
b ) We know that y² = 4x ⇒
r²sin²(θ) = 4r cos(θ),
r = 4cos(θ) / sin²(θ) = 4 cot(θ) csc(θ) = 4cotθcscθ - again the correct solution is option c
Write the equation of the line that passes through (−2, 6) and (2, 14) in slope-intercept form. (2 points)
Answer:
[tex]y = 4x + 14[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation we must first find the slope of the line
Slope of the line using points (−2, 6) and (2, 14) is
[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]
Now we use the slope and any of the points to find the equation of the line.
Equation of the line using point ( - 2, 6) and slope 4 is
[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]
We have the final answer as
[tex]y = 4x + 14[/tex]
Hope this helps you
There are $400$ pages in Sheila's favorite book. The average number of words per page in the book is $300$. If she types at an average rate of $40$ words per minute, how many hours will it take to type the $400$ pages of the book?
Answer:
50hours
Step-by-step explanation:
Given that there are 400 pages in Sheila's favorite book.
The average number of words per page in the book is 300
She types an average rate of 40words per minute.
So to type 400pages of the book
Total number of words in the pages = 400×300 = 120000 words
Typing rate : 40words ------- 1minute
120000 words ----------- x minutes
Hence we have 40 × X mins = 120000 × 1min
Make X the subject
40X = 120000minutes
X = 120000/40
X = 3000minutes
Since 60minutes = 1hour
3000minutes = 3000minutes/60
= 50hours
Hence it took her 50hours to type 400pages
Solution:
The total number of words in the book is 400 x 300. Sheila types at a rate of 40 words per minute, or 40 x 60 words per hour. The number of hours it takes her is equal to the number of words divided by her rate of typing, or 400x300/40x60 = 50 hours.
Given g(x) = -x - 2, find g(3).
Answer:
g(3) = -5
Step-by-step explanation:
g(3) is basically the value of g(x) when x = 3. Therefore, g(3) = -3 - 2 = -5.
Answer:
[tex] \boxed{\sf g(3) = -5} [/tex]
Given:
g(x) = -x - 2
To Find:
g(3) i.e. g(x) where x = 3
Step-by-step explanation:
[tex]\sf Evaluate \ -x - 2 \ where \ x = 3:[/tex]
[tex] \sf \implies - x - 2 = - 3 - 2[/tex]
[tex] \sf - 3 - 2 = - (3 + 2) : [/tex]
[tex] \sf \implies - (3 + 2)[/tex]
[tex] \sf 3 + 2 = 5 : [/tex]
[tex] \sf \implies - 5[/tex]
find the derivative of f(x)=3x^2✓x
Answer:
[tex]f'(x)=\dfrac{15x\sqrt{x}}{2}[/tex]
Step-by-step explanation:
The power rule applies.
d(x^n)/dx = nx^(n-1)
__
[tex]f(x)=3x^2\sqrt{x}=3x^{\frac{5}{2}}\\\\f'(x)=3(\frac{5}{2})x^{\frac{3}{2}}\\\\\boxed{f'(x)=\dfrac{15x\sqrt{x}}{2}}[/tex]
A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are as follows: 22 17 27 20 23 19 24 18 19 24 We want to determine at the 5% significance level that the population mean is not equal to 20. What is the rejection region?
Answer:
0.09
Step-by-step explanation:
Let x = ages of mother
x : 22 17 27 20 23 19 24 18 19 24
N = 10
Mean = ∑x/N = 218/10 = 21.8
Difference in mean = 21.8 - 20 = 1.8
If significance level = 5% or 0.05
∴ Rejection region = 1.8 X 0.05 = 0.09
Lydia drives from city a to city b to transport goods. her return speed is 3 times her departure speed and she takes 40 minutes less on her return trip. how long did her departure trip take?
Answer:
1 hour
Step-by-step explanation:
Hello, let's say that her departure trip takes t in minutes, as her return speed is 3 times her departure speed, she took t/3 for the return and we know that this 40 minutes less, so we can write.
t/3=t-40
We can multiply by 3
t = 3t -40*3 = 3t - 120
This is equivalent to
3t -120 = t
We subtract t
2t-120 = 0
2t = 120
We divide by 2
t = 120/2 = 60
So this is 60 minutes = 1 hour.
Thank you.
Is the quotient of two rational numbers always a rational number? Explain.
Answer:
Yes,
Step-by-step explananation
The quotient of two rational numbers is always rational, and the reason for this lies in the fact that the product of two integers is always an rational number.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
From Algebra, we know that a Rational Number is a Real Number of the form:
[tex]x = \frac{a}{b}[/tex], [tex]a, b\in \mathbb{N}[/tex], [tex]x \in \mathbb{R}[/tex] (1)
Where:
[tex]a[/tex] - Numerator.[tex]b[/tex] - Denominator.[tex]x[/tex] - Quotient.The Quotient can be an Integer or not. In the first case, all Quotients have their equivalent Rational Numbers.
Now, if we divide a Rational Number by another Rational Number, then we have the following expression:
[tex]x' = \frac{x_{1}}{x_{2}}[/tex]
If [tex]x'[/tex] is a Rational Number, then it must also an Integer and if [tex]x'[/tex] is an Integer, then [tex]x_{1}[/tex] and [tex]x_{2}[/tex] must be Multiples of each other.
The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.
Please see this question related to Rational Numbers: https://brainly.com/question/24398433
Given that
[tex]\sqrt{2p-7}=3[/tex]
and
[tex]7\sqrt{3q-1}=2[/tex]
Evaluate
[tex]p + {q}^{2} [/tex]
Answer:
Below
Step-by-step explanation:
The two given expressions are:
● √(2p-7) = 3
● 7√(3q-1) = 2
We are told to evaluate p+q^2
To do that let's find the values of p and q^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's start with p.
● √(2p-7) = 3
Square both sides
● (2p-7) = 3^2
● 2p-7 = 9
Add 7 to both sides
● 2p-7+7 = 9+7
● 2p = 16
Divide both sides by 2
● 2p/2 = 16/2
● p = 8
So the value of p is 8
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Let's find the value of q^2
● 7√(3q-1) = 2
Square both sides
● 7^2 × (3q-1) = 2^2
● 49 × (3q-1) = 4
● 49 × 3q - 49 × 1 = 4
● 147q - 49 = 4
Add 49 to both sides
● 147q -49 +49 = 4+49
● 147q = 53
Divide both sides by 147
● 147q/147 = 53/147
● q = 53/ 147
Square both sides
● q^2 = 53^2 / 147^2
● q^2 = 2809/21609
■■■■■■■■■■■■■■■■■■■■■■■■■
● p+q^2 = 8 +(2809/21609)
● p+q^2 = (2809 + 8×21609)/21609
● p+q^2 = 175681 / 21609
● p + q^2 = 8.129
Round it to the nearest unit
● p+ q^2 = 8
F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23
Answer:
∠ H ≈ 23°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus
∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5 . If there were 4545 no votes, what was the total number of votes?
Answer:
The total number of votes= 9999
Step-by-step explanation:
The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.
There is a total of 4545 no votes.
Yes/no = 6/5
Yes= no(6/5)
Yes= 4545(6/5)
Yes= 5454
The total number of yes votes are 5454.
The total number of votes= yes votes+ no votes
The total number of votes= 5454+4545
The total number of votes= 9999
What Number is equivalent to 4^3
A. 7
B. 12
O C. 64
D. 81
Answer:
C
Step-by-step explanation:
4³ means 4 multiplied by itself 3 times, that is
4 × 4 × 4
= 16 × 4
= 64 → C
Manuel says that he can solve the equation 3n = 21 by multiplying both sides by ⅓. Explain why this is correct.
Step-by-step explanation:
はい、両側を削除して、3を掛けて7にします
Step-by-step explanation:
Given:
3n = 21
if we multiply both sides by 1/3, we will get:
3n = 21
3n x (1/3)= 21 x (1/3)
3n/3 = 21/3
n = 21/3
n = 7
Hence we can indeed solve for n by multiplying both sides by (1/3)
A special mixed-nut blend at a store cost $1.35 per lb, and in 2010 the blend cost $1.83 per lb. Let y represent the cost of a pound of the mixed-nut blend x years after 2005. Use a linear equation model to estimate the cost of a pound of the mixed-nut blend in 2007.
Answer:
y = $1.542 per lb
Step-by-step explanation:
given data
mixed-nut blend store cost 2005 = $1.35 per lb
blend cost in 2010 = $1.83 per lb
solution
we consider here y = cost of a pound
and x year = after 2005
we will use here linear equation model
so
[tex]\frac{y - 1.35}{1.83-1.35} = \frac{x-10}{5 - 0}[/tex] .........................1
solve it we get
5y - 6.75 = .48 x
so
at 2007 year here x wil be 2
so
[tex]y = \frac{0.48 \times 2 + 6.75}{5}[/tex]
solve it we get
y = $1.542 per lb
Combine like terms to simplify the expression: 2/5k - 3/5 +1/10k
━━━━━━━☆☆━━━━━━━
▹ Answer
1/2k - 3/5
▹ Step-by-Step Explanation
2/5k - 3/5 + 1/10k
Collect like terms:
2/5k + 1/10k = 1/2
Final Answer:
1/2k - 3/5
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
1/2k - 3/5
Step-by-step explanation:
Hey there!
Well the only fraction needed to combine are,
2/5 and 1/10.
To add them we need to make 2/5 have a denominator of 10.
To do that we multiply 5 by 2.
5*2 = 10
What happens to the denominator happens to the denominator.
2*2 = 4
Fraction - 4/10
4/10 + 1/10 = 5/10
5/10
simplified
1/2
1/2k - 3/5
Hope this helps :)
a is less than or equal to 10
Lmk
Answer:
[tex]a \leqslant 10[/tex]
Step-by-step explanation:
a is less than or equal to 10
less than: <
equal: =
less than or equal to: ≤
Hope this helps ;) ❤❤❤
hope it helps you
imp=draw dark shaded point in thqt line and point towards left
An artifact was found and tested for its carbon-14 content. If 72% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years).
Answer:
2700 years
Step-by-step explanation:
The exponential function for the fraction remaining is ...
r(t) = (1/2)^(t/5730)
where r is the remaining fraction and t is the time in years. We can solve for t to get ...
log(r) = (t/5730)log(1/2)
t = 5730·log(r)/log(1/2)
For the given r=0.72, the age of the artifact is estimated to be ...
t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years
Solve for x -3x-3=-3(x+1)
Step-by-step explanation:
[tex] - 3x - 3 = - 3(x + 1) \\ - 3x - 3 = - 3x - 3 \\ - 3x + 3x = - 3 + 3 \\ 0 = 0[/tex]
Step 1: Use 3 to open the bracket
Step 2 : Collect like terms and simplify
Answer = 0
What is 1/3 of 675 is left
Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −4 is the only other zero, leading coefficient is 4. setup problem so I can solve, thanks!!
Answer:
Step-by-step explanation:
Hello,
degree 5
4 is a zero of multiplicity 3 -> (x-4)^3 is a factor
-4 is the only other zero, so the multiplicity is 5-3=2 -> (x+4)^2 is a factor
leading coefficient is 4 so we can write
[tex]\boxed{4(x-4)^3(x+4)^2}[/tex]
If there is something that you do not understand or you are blocked somewhere let us know what / where.
Thank you.
Given v(x) = g(x) (3/2*x^4 + 4x – 1), find v'(2).
Answer:
Step-by-step explanation:
Given that v(x) = g(x)×(3/2*x^4+4x-1)
Let's find V'(2)
V(x) is a product of two functions
● V'(x) = g'(x)×(3/2*x^4+4x-1)+ g(x) ×(3/2*x^4+4x-1)
We are interested in V'(2) so we will replace x by 2 in the expression above.
g'(2) can be deduced from the graph.
● g'(2) is equal to the slope of the tangent line in 2.
● let m be that slope .
● g'(2) = m =>g'(2) = rise /run
● g'(2) = 2/1 =2
We've run 1 square to the right and rised 2 squares up to reach g(2)
g(2) is -1 as shown in the graph.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's derivate the second function.
Let h(x) be that function
● h(x) = 3/2*x^4 +4x-1
● h'(x) = 3/2*4*x^3 + 4
● h'(x) = 6x^3 +4
Let's calculate h'(2)
● h'(2) = 6 × 2^3 + 4
● h'(2) = 52
Let's calculate h(2)
●h(2) = 3/2*2^4 + 4×2 -1
●h(2)= 31
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Replace now everything with its value to find V'(2)
● V'(2) = g'(2)×h(2) + g(2)× h'(2)
● V'(2)= 2×31 + (-1)×52
●V'(2) = 61 -52
●V'(2)= 9
