Slope intercept form of the equation 4x + 5y = - 30 is written as,
⇒ y = - 4/5x - 6
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The equation is,
⇒ 4x + 5y = - 30
Now, We know that;
Slope intercept form of the equation is,
⇒ y = mx + c
Here, The equation is,
⇒ 4x + 5y = - 30
Subtract 4x both side,
⇒ 4x + 5y - 4x = - 30 - 4x
⇒ 5y = - 4x - 30
Divide by 5 both side, we get;
⇒ y = - 4/5x - 6
Hence, The Slope intercept form of the equation is,
⇒ y = - 4/5x - 6
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If h(x) = g[f(x)], use the table of values for f, g, f'and g' to find the value of h'(1).
x f(x) g(x) f'(x) g'(x)
1 3
2
2
6
2 1
00
5
7
3
7
2
7
9
your answer goes here
Answer:
Hey there :)
h ( x ) = f [ g ( x ) ]
To find h ' ( x )
We do → f ' [ g ( x ) ] × g ' ( x )
This is called the chain rule
Given;
g ( 1 ) = 2 → f ' ( 2 ) = 5
g ' ( 1 ) = 6
Apply the formula
h ' ( 1 ) = f ' [ g ( 1 ) ] × g ' ( 1 )
= f ' ( 2 ) × 6
= 5 × 6
h ' ( 1 ) = 30
If h(x) = g[f(x)], the value of h'(1) from the given table is calculated as 18.
To find the value of h'(1), we need to apply the chain rule. The chain rule states that if we have a composite function h(x) = g[f(x)], then its derivative h'(x) is given by [tex]\(h'(x) = g'(f(x)) \cdot f'(x)\)[/tex].
Let's use the table of values to find h'(1):
1. f(1) = 3
2. g(f(1)) = g(3) = 2
3. f'(1) = 2
4. g'(f(1)) = g'(3) = 9
Now, we can find h'(1) using the chain rule:
[tex]\[h'(1) = g'(f(1)) \cdot f'(1) = 9 \cdot 2 = 18.\][/tex]
Therefore, the value of h'(1) is 18.
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A soup recipe makes 6 cups. How many people does it serve if each serving is 3/4 of a cup?
6
10
8
4
Answer: 8
please see below for work!
On a photograph an ant is enlarged at a scale 25:1. In the photo, the ant's leg is 15 cm. What is the actual length of the ant's leg?
Answer:
3/5cm
Step-by-step explanation:
Let's solve your equation step-by-step.
x(25)=15
Step 1: Simplify both sides of the equation.
25x=15
Step 2: Divide both sides by 25.
25x /25 = 15/25
x = 3/5
Actual length of ant's leg is 0.6cm
Let the actual length of ant's leg = a
Scale = 25 : 1
Length in photo = 15 cm
Express as a an equation :
25 × actual length = 1 × length in photo
25a = 15
a = 15 / 25
a = 0.6
Hence, actual length of ant's leg is 0.6cm
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You walking against the wind. Your normal speed without the wind is 5mph. How long will it takes you to cover a distance of 5miles if the wind slow you down to 4/5 of your normal speed?
Answer:
1.25 hours
Step-by-step explanation:
So if you walk at 5 mph without wind, it takes you 1 hour to cover a 5 mile distance since you travel at a speed of 5 every hour. (5 mph). with the wind, your speed is 4 miles per hour because the wind slows you down to 4/5ths of your normal speed. 4/5ths of 5 is 4. It takes 1.25 hours to walk with the wind because 5(miles)/4(mph) is 1.25 hours. Hope this helps bud!
Find the value for
20:5=30:X
Answer: 6
Step-by-step explanation:
20/5 = 30/x
5 = 30/x
x = 6
The value 'x' in the given equation is 7.5.
What is the ratio of two numbers?"Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B."
Given, 20:5=30:X
⇒ [tex]\frac{20}{5} = \frac{30}{x}[/tex]
⇒ x = (30 × 5) / 20
⇒ x = 7.5
Therefore, the value of x is 7.5.
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Solve for g.
g + (-5) = 27
answer: g=32 u should simplify
The value of a school bus reduces from $512000 to $343000in 3 years. Find the
uniform rate of depreciation per annum (R).
Answer:
The uniform rate of depreciation is $56,333 per year, or 11% per year.
Step-by-step explanation:
Rate of Depreciation
If some object has a certain value P and after some time t its value decreases to Q, the rate of depreciation is a measure of how much its value changed per unit time.
It can be calculated as:
[tex]\displaystyle R=\frac{P-Q}{t}[/tex]
It can also be expressed as a percentage, dividing the previous value by P.
The school bus reduces its value from $512,000 to $343,000 in 3 years, thus:
[tex]\displaystyle R=\frac{512,000-343,000}{3}[/tex]
[tex]\displaystyle R=\frac{169,000}{3}[/tex]
R = 56,333 $/year
Expressed as a percentage:
R = 56,333 / 512,000 = 0.11
R = 11%/year
The uniform rate of depreciation is $56,333 per year, or 11% per year.
Which of the following equations represent linear functions?
y=x2−3x
4x+y=5
y=|2x+1|
y=−5
Answer:
its y=-5x
Step-by-step explanation:
Why?
linear functions have only the slope, they dont include the y-intercept
Find the y-intercept of the folowing equation. Simplify your answer
19x + 8y=7
Answer:
y-intercept occurs when x = 0
19x + 8y=7
19*0 + 8y = 7
y -intercept = (0, 7/8)
Step-by-step explanation:
At the middle school Vanessa attends, there are 240 Grade 6 students, 210 Grade students, and 200 Grade 8 students. Which ratio best compares the number of tudents in Grade 8 to the number of students in Grade 6 at Vanessa's school? A 5:6 ® 5:11 © 6:5 07:8
Answer:
A, 5:6
Step-by-step explanation: :)
Answer:
YAH IM CONFUSEDDD
Step-by-step explanation:
help please!!!!! (QUESTION #3)!!!!!!!
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE ANSWERRRRRRRRRRRRRRRRRRRR FASTTTTTTTTTTTTTTTTTT WILL GIVE BRAINLIST. PLEASEEEEEEEEEEEE
Suppose that the age of all the U.S. first ladies when they married was recorded. The mean age of U.S. first ladies when they married would be a:________A) PopulationB) StatisticC) SampleD) Parameter
Answer:
B) Statistic
Step-by-step explanation:
The mean age of U.S. first ladies when they married would be a Statistic. This is because the mean age would be a specifically targeted value of the population that is being analyzed. In this scenario, the population would be all of the First Ladies, while the Sample would be the data gathered from the population under certain parameters. Statistics can be a variety of different values that revolve around the samples gathered such as average age, average height, max number of blue-eyed First Ladies, etc.
What is the correct number form for “one and twenty-five thousandths.”
The correct number form for “one and twenty-five thousandths.” is 1.025.
What is a place value?A place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.Twenty-five (25) thousandths as a decimal can be written as follows:
Decimal = 25/1000
Decimal = 0.025.
Combining the word sentence "one and twenty-five thousandths," we have:
Number = 1.025.
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Please help with the problem in the picture ^ I’ll give brainliest if you give me a small explanation! :)
Answer:
it is c if you add 2x8 wich makes 16
can u pls help me with this question
Rebekah has $400 to spend on a video game system and games. The system cost $289.99 and each game costs $32.29. How many games can she buy with the game system?
A. No more than 2 games
B. No more than 3 games
C. No more than 4 games
D. No more than 5 games
PLEASE HELP FAST!!!!!!!
Answer:
B) No more than three games
Step-by-step explanation:
est $290+32=322
322+32+32=$386
386+32=418 (which is over price)
Answer:
B. no meor than three games
Step-by-step explanation:
400.00 - 289.99 = 110.01
110.01 - 32.29 = 72.72 (1 game)
72.27 - 32.29 = 45.43 (2 games)
45.43 - 32.29 = 13.14 (3 games)
13.14 left over
What value of b will cause the system to have an
infinite number of solutions?
6
y = 6x-b
+3x+12y=-3
-3x + y = -3
b =
Answer: b=6
Step-by-step explanation:
I hope this helps on edge
To make the system have an infinite number of solutions, the value of b can be any real number.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
For the system to have an infinite number of solutions, the two equations must be dependent, which means that one of the equations can be obtained by a linear combination of the other two equations.
So,
Let's rearrange the given equations into the slope-intercept form:
y = 6x - b _____(1)
3x + 12y = -3 ______(2)
-3x + y = -3 ______(3)
From equation (3),
y = 3x - 3 _______(4)
Now,
We can see that equation (1) is a multiple of equation (4) with a slope of 6/3 = 2.
Specifically, equation (1) can be obtained by multiplying equation (4) by 2 and then subtracting b from both sides.
So,
2(3x - 3) - b = 6x - b
Simplifying this expression.
6x - b = 6x - b
Since this equation is true for any value of x and b, we have an infinite number of solutions.
Therefore,
To make the system have an infinite number of solutions, the value of b can be any real number.
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On the first circle, what segment is a diameter? How long is it?
Answer:
The segment that is the diameter is EB
It is 8 cm long
Step-by-step explanation:
riddle #2
I am a five digit even number.
all of my digits are factor of 24.
4/5 of my digits are even.
The digit in my thousands place equals the perimeter of a 2×2 array.
The digits in my ten thousand places is twice the value of the digits in the hundreds place, but half the value of the digits in the thousands places.
The digit in my tens places equal the number of lines of symmetry in an isosceles triangle.
Answer:
28416
Step-by-step explanation:
No digits can be repeated
"All my digits are factors of 24" This means that the possible digits are: 1, 2, 3, 4, 6, 8
"The digits in my thousands place equals the perimeter of a 2x2 array" That would be 8
"The digits in my ten thousand places is twice the value of the digits in the hundreds place, but half the value of the digits in the thousands place" That would be 4, which also means that the ten thousands place is 2
"The digits in my tens place equal the number of lines of symmetry in an isoceles triangle" There is only 1 lines of symmetry
This means that we have 2841(?)
Because this number is even and no digits can be repeated, the only possible digits from those available is 6
Therefore the number is 28416
Jane gets paid $120 for 8 hours. How much does she get paid an hour?
Answer:
$15 an hour
Step-by-step explanation:
To find this, we divide 120 by 8.
120 ÷ 8 = 15
So Jane gets $15 an hour
I hope this helped, please mark Brainliest, thank you!
A bookcase has 5 of these bookshelves that are 42 inches long. How many FEET of shelf space is there? Explain your reasoning. (If the answer is given in inches you can only get a 4 out of 6 maximum. How many FEET of shelf space is the answer you explain.) *
Answer:
[tex]17.5\ \text{feet}[/tex]
Step-by-step explanation:
A bookcase has 5 bookshelves. Each bookshelf is 42 inches long.
Total bookshelf length in the book case = [tex]5\times 42=210\ \text{inches}[/tex]
[tex]1\ \text{feet}=12\ \text{inches}\\\Rightarrow 1\ \text{inch}=\dfrac{1}{12}\ \text{feet}[/tex]
[tex]210\ \text{feet}=210\times \dfrac{1}{12}=17.5\ \text{feet}[/tex]
The bookcase has a total shelf space of [tex]17.5\ \text{feet}[/tex].
*One bookshelf has a space of [tex]\dfrac{42}{12}=3.5\ \text{feet}[/tex].
no one helps me bruh....
Answer:
I'm sorry I just dont know it....
What is the value of x in the proportion below?
1/2 / 4 = x/28
3 1/2
7 1/2
14
56
Answer:
A 3 1/2
Step-by-step explanation:
There are a number of ways that you can solve this
Method 1)
Since these proportions are set equal to each other, we know that x is also equivalent to 1/2. So, we need to find the whole-number that was multiplied by the first fraction (1/2/4) that gave us the second fraction (x/28).
So we need to divide the denominators
28/4 = 7
Now that we have that number, we will mutiply 1/2 by it because we know that whatever x is the 1/2 times 7 since 28 is 4*7:
1/2 * 7 = 3.5 or 3 1/2, so 3 1/2 is our answer...
Another way that we can solve this is by using the cross product (butterfly method)
Method 2)
Multiply 28 by 1/2 = 14.
Now we will divide 14 by 4. 14/4 = 3.5
3.5 = 3 1/2, so that is our answer.
Please answer i wanna get this over with h ^-2 / h ^4
Answer:
= h^-6
Step-by-step explanation:
When dividing powers you subtract them (indices rules)
--> -2 - 4 = -6
Hope this helps, please mark as brainliest
Morning can someone help me please and can you please let me know how you got the answer
Answer:
The customary system states that one pound is equivalent to sixteen ounces(oz).
Step-by-step explanation:
Since the package is one pound, it contains sixteen ounces(oz).
7x31=????????????????
Answer:
217
Step-by-step explanation:
7 × 31 = 217I hope this helps!
y - 2/5 = 1 3/5 (plz show work)
Answer:
y=2
Step-by-step explanation:
that's the answer hope u understand it
Answer:
[tex]y = 2[/tex]
Step-by-step explanation:
Sure.
[tex]y - \frac{2}{5} = 1 \frac{3}{5} \\[/tex]
Convert to improper fraction
[tex]y - \frac{2}{5} = \frac{8}{5}[/tex]
Combine like terms
[tex]y - \frac{2}{5} = \frac{8}{5} \\[/tex]
[tex]+\frac{2}{5}[/tex] from both sides
[tex]y = \frac{8}{5} + \frac{2}{5} \\y = 2[/tex]
Love from Nepal :)
What is the equation, in slope-intercept form, of the line
that is perpendicular to the given line and passes through
the point (2, -1)?
A)y = -1/3 x -1/3
B)y = -1/3 x -5/3
C)y = 3x - 3
D)y = 3x - 7
Answer:
My guess would be D.
Step-by-step explanation:
We can eliminate A and B right away considering the Slope of the first equation is already -1/3 and we need the slope to be opposite to be perpendicular. So right then It is either C or D. and with C It doesn't seem like the line intersecting the line above would be parallel so my guess is D.
Determine the sample size required to estimate a population mean to within 10 units given that the population standard deviation is 60. A confidence level of 90% is judged to be appropriate.
Answer: 98
Step-by-step explanation:
Formula to find sample size if population standard deviation is known:
[tex]n=(\dfrac{z^c\times\sigma}{E})^2[/tex] , where [tex]\sigma=[/tex]population standard deviation, [tex]z^c[/tex] =Critical z-value for confidence level, E= Margin of error.
Given: [tex]\sigma=30,\ \ \ E=10[/tex]
Critical z-value for 90% confidence = 1.645
[tex]n=(\dfrac{1.645\times60}{10})^2\\\\=(1.645\times6)^2\\\\=9.87^2\\\\=97.4169\approx98[/tex]
Required minimum sample size = 98