d = st
if speed is constant, there is a proportional relation between distance (d) and time (t). The constant (s) can be defined as:
s = d/t
and you can compute it knowing the distance travelled in some time
if time is constant, there is a proportional relation between distance (d) and speed (s). The constant (t) can be defined as:
t = d/s
and you can compute it knowing the distance travelled at some speed.
Acceleration (a) is defined as:
a = s/t
this equation can be rewritten as:
s = at
where a is the constant of proportionality.
Another example is Hook's law, which states:
F = ke
where F is the force applied to a spring, k is the spring constant, and e is the extension of the spring.
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (2, −1), and Monique's desk is located at (−2, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
square root of 10 feet
square root of 20 feet
square root of 52 feet
square root of 104 feet
Answer:
√52 feet
Step-by-step explanation:
5 - -1 = 6
-2 - 2 = -4
6 = change in y
-4 = change in x
a² + b² = c² (pythagoras theorem)
6² = 36
-4² = 16
36 + 16 = 52
c² = 52
c = √52
Answer: square root of 52 feet
A sequence is generated by An= -2n - 4, find the 5 terms of the sequence
William, this is the solution:
An= -2n - 4
A1 = -2 * 1 - 4
A1 = -6
A2 = -2 * 2 - 4
A2 = -4 - 4
A2 = -8
A3 = -2 * 3 - 4
A3 = -6 - 4
A3 = -10
A4 = -2 * 4 - 4
A4 = -8 - 4
A4 = - 12
A5 = -2 * 5 - 4
A5 = -10 - 4
A5 = - 14
- 10x + 100y = 30-3x + 30y = 9
The given system is
[tex]\mleft\{\begin{aligned}-10x+100y=30 \\ -3x+30y=9\end{aligned}\mright.[/tex]First, we multiply the first equation by -3/10.
[tex]\mleft\{\begin{aligned}3x-30y=-9 \\ -3x+30y=9\end{aligned}\mright.[/tex]Then, we sum the equations
[tex]\begin{gathered} 3x-3x+30y-30y=9-9 \\ 0x+0y=0 \\ 0=0 \end{gathered}[/tex]According to this result, we can deduct that the system doesn't have any solutions because the lines represented by the equations are parallel.The function c(x) = 50x represents the number of words c(x) you can type in x minutes. How many words can you type in 6.5 minutes? PLEASE HELP!
Given the function c(x) = 50x where c (x) is the number of words. In 6.5 minutes, the number of words that can be typed is
= 50 * 6.5
= 325 words
identify the maximum from the tabletype your answer as an ordered pair (x,y)
We want to know the maximum value for f(x). In this case, we have that when f(x) = 10, x =6. Then, the ordered pair (6,10) represents the maximum from the table
what are the bounds of integration for the first integral ?
We are going to use the properties of definite integrals. Note that if c belongs to the interval [a,b] and is integrable in [a,c] and [c,b], then f is integrable in [a,b]. Moreover,
[tex]\int_a^cf(x)dx+\int_c^bf(x)dx=\int_a^bf(x)dx[/tex]Applying this property to the presented case, we obtain that
[tex]\begin{gathered} \int_a^bf(x)dx=\int_{-5}^9f(x)dx+\int_9^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_{-5}^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_2^{13}f(x)dx \end{gathered}[/tex]Note: Another way to interpret the exercise is to interpret the integral as the area under the curve.
Thus, the answer to the exercise is a= 2 and b = 13.
Using the figure, determine the length, in units, of LM
Given the coordinates of L and M
To get the length between the two coordinates, we will follow the steps below
Step 1: List out the coordinates of L and M
[tex]L(-4,-3)[/tex][tex]M(-4,4)[/tex]step 2: calculate the distance
Since they both have the same x coordinates, we can simply subtract the y-coordinate of L from M
[tex]M-L=4-(-3)=4+3=7[/tex]Therefore, the distance LM is 7 units
Use a unit multiplier to convert 90 meters per minute to meters per second.
Hello there. To solve this question, we'll have to remember some properties about unit conversions.
We want to convert 90 meters per minute to meters per second.
Remember 1 minute is equal to 60 seconds, therefore we can write
90 meters per 60 seconds
Simplify it by a factor of 30
3 meters per 2 seconds
Which is the same as
1.5 meters per second
The unit multiplier was divide the number by 60, in order to get minutes to seconds and, therefore, find the value in m/s.
The equation and graph of a polynomial are shown below. The graph reachesits minimum when the value of xis 4. What is the y-value of this minimum?--y= 2x2-16x + 30ys
We can find the y-value of the minimum using the graph or using the equation. Let's use the equation and evaluate it when x = 4.
[tex]\begin{gathered} y=2x^2-16x+30=2(4)^2-16(4)+30 \\ y=2\cdot16-64+30=32-64+30=-2 \end{gathered}[/tex]Hence, the y-value of the minimum is -2.5. Given the degree and zeros of a polynomial function, find the standard form of the polynomial.
Degree: 5; zero: 1, i, 1+i
The expanded polynomial is:
x5 +
x4+
x3 +
x2 +
x +
The equation of the polynomial equation in standard form is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
How to determine the polynomial expression in standard form?The given parameters are
Degree = 5
Zero = 1, i, 1 + i
There are complex numbers in the above zeros
This means that, the other zeros are
Zeros = 1 - i and -i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = (x - 1) * (x - (1 + i)) * (x - (1 - i) * (x - (-i)) * (x - i)
This gives
P(x) = (x - 1) * (x - 1 - i) * (x - 1 + i) * (x² + 1)
Solving further, we have
P(x) = (x - 1) * (x² - x + ix - x + 1 - i - ix + i + 1) * (x² + 1)
P(x) = (x - 1) * (x² - 2x + 2) * (x² + 1)
Evaluate the products)
P(x) = (x³ - x² + x - 1) * (x² - 2x + 2)
This gives
P(x) = x⁵ - 2x⁴ + 2x³ - x⁴ + 2x³ - 2x² + x³ - 2x² + 2x - x² + 2x - 2
Express in standard form
P(x) = x⁵ - 2x⁴ - x⁴ + 2x³ + 2x³ + x³ - 2x² - 2x² - x² + 2x + 2x - 2
Evaluate the like terms
P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
Hence, the equation is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
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Find the equation of a line perpendicular to y + 1 =-1/2xthat passesthrough the point (-8, 7).
step 1
Find out the slope of the given line
we have
y+1=-(1/2)x
The slope is m=-1/2
Remember that
If two lines are perpendicular
then
their slopes are negative reciprocal
so
The slope of the perpendicular line is
m=2
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=2
point (-8,7)
substitute and solve for b
7=2(-8)+b
7=-16+b
b=23
therefore
the equation of the line is
y=2x+23what would be the most appropriate domain for this function? Number 7
Explanation:
This function is C(n) which means it's a function of n. It is said that n is the number of observed vehicles in a specified time interval. It cannot be negative and it has to be an integer. Therefore the domain is all integers greater or equal than zero.
Answer:
4) {0, 1, 2, 3...}
A) This graph represents Function or non function?B) is it discrete or Continuous?Because of you count dots or measure lines?The domain is:The range is:
A) It's a function because each point of x has a point on y.
B. It's a discrete functions because you can't see a continuous line.
C. Domain (-3,6)
D. Range (0,3)
* C and D if each square is equivalent to 1 unit.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p-10.1=6.5p-4-0.01p? Select two options
Given:
Given the equation
[tex]2.3p-10.1=6.5p-4-0.01p[/tex]Required: Rewrite the given equation.
Explanation:
Take the common coefficients of p and add the constants.
[tex]\begin{gathered} 2.3p-10.1-6.5p+4+0.01p=0 \\ (2.3-6.5+0.01)p+(4-10.1)=0 \\ -4.19p-6.1=0 \\ 4.19p+6.1=0 \end{gathered}[/tex]Final Answer: The given equation can be rewritten as 4.19p+6.1 = 0
2. Does the data describe a positive or negative correlation? (1/2 point)3. Find the equation of your line of fit. (1 point)+4. What predicted vehicle weight would indicate a vehicle whose gas mileage is 30 miles per gallon?(1 point)5. Suppose you have a vehicle that weighs 1500 pounds. Use the model to determine the expected city MPGof the vehicle. (1 point)
Given the values shown in the table, let be "x" the Vehicle weight (in hundreds of lbs.) and "y" the City MPG (Miles per gallon).
1. Given the points:
[tex](27,25),(35,19),(39,16),(32,21),(40,15),(23,29),(18,31),(37,15),(17,46),(23,26),(37,17),(30,26),(23,29),(32,19),(20,33),(30,21)[/tex]You can plot them on a Coordinate Plane:
2. Notice the following line:
Notice that the points are closed to the red line that has a negative slope. Therefore, you can identify that when one of the variables increases, the other variable decreases. Hence, you can conclude that the data describes a negative correlation.
3. You need to follow these steps to find the equation of the line of best fit:
- You need to find the average of the x-values by adding them and dividing the Sum by the number of x-values:
[tex]\bar{X}=\frac{27+35+39+32+40+23+18+37+17+23+37+30+23+32+20+30}{16}[/tex][tex]\bar{X}=28.9375[/tex]- Find the average of the y-values:
[tex]\bar{Y}=\frac{25+19+16+21+15+29+31+15+46+26+17+26+29+19+33+21}{16}[/tex][tex]\bar{Y}=24.25[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{X})[/tex]Where this represents each x-values in the data set:
[tex]x_i[/tex]You get:
[tex]\sum_{i=1}^n(x_i-\bar{X})=(27-28.9375)+(35-28.9375)+(39-28.9375)+(32-28.9375)+(40-28.9375)+(23-28.9375)+(18-28.9375)+(37-28.9375)+(17-28.9375)+(23-28.9375)+(37-28.9375)+(30-28.9375)+(23-28.9375)+(32-28.9375)+(20-28.9375)+(30-29.9375)[/tex][tex]\sum_{i=1}^n(x_i-\bar{X})=1.0625[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{Y})[/tex]You get:
[tex]\sum_{i=1}^n(x_i-\bar{Y})=(25-24.25)+(19-24.25)+(16-24.25)+(21-24.25)+(15-24.25)+(29-24.25)+(31-24.25)+(15-24.25)+(46-24.25)+(26-24.25)+(17-24.25)+(26-24.25)+(29-24.25)+(19-24.25)+(33-24.25)+(21-24.25)[/tex][tex]\sum_{i=1}^n(x_i-\bar{Y})=-3.25[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{X})(y_i-\bar{Y})[/tex]You get:
[tex]=-857.75[/tex]- Find:
[tex]\sum_{i=1}^n(x_i-\bar{X})^2[/tex]You can find it by squaring each Difference of the x-values and the Mean. you get:
[tex]=862.9375[/tex]- Find the slope of the line
[tex]m=\frac{-857.75}{862.9375}\approx-0.994[/tex]- Find the y-intercept with this formula:
[tex]b=\bar{Y}-m\bar{X}[/tex][tex]b=24.25-(-0.994)(1.0625)[/tex][tex]b=53.0135[/tex]Therefore, the line in Slope-Intercept Form:
[tex]y=mx+b[/tex]is the following:
[tex]y=-0.9940x+53.0135[/tex]4. If:
[tex]y=30[/tex]You can predict the vehicle weight by substituting that value into the equation found in Part 3, and solving for "x":
[tex]30=-0.9940x+53.0135[/tex][tex]\frac{30-53.0135}{-0.9949}=x[/tex][tex]x\approx23.1524[/tex]5. If a vehicle weighs 1500 pounds, then:
[tex]x=1500[/tex]Then you can determine the expected city MPG of the vehicle by substituting this value into the equation and evaluating:
[tex]y=-0.9940(1500)+53.0135[/tex][tex]y\approx-1437.9865[/tex]Hence, the answers are:
1.
2. It describes a negative correlation.
3.
[tex]y=-0.9940x+53.0135[/tex]4.
[tex]x\approx23.1524\text{ \lparen in hundreds of pounds\rparen}[/tex]5.
[tex]y\approx-1437.9865\text{ \lparen In miles per gallon\rparen}[/tex]
I need help with the calculus portion of my ACT prep guide
The first thing we have to do is find the pascal coefficients of the triangle for this we use the following image
From our exercise we know that
[tex]\begin{gathered} (2x^3-3y)^3\to(a+b)^3 \\ a=2x^3 \\ b=-3y \end{gathered}[/tex]Then our coefficients of Pascal's triangle are 1 - 3 - 3 - 1
Using the right triangle we get:
[tex]1a^3+3a^2b+3ab^2+1b^3[/tex]We substitute the values of a and b in our new expression to find our solution
[tex]1(2x^3)^3+3(2x^3)^2(-3y)+3(2x^3)(-3y)^2+1(-3y)^3[/tex][tex]\begin{gathered} 8x^9+3(4x^6)^{}(-3y)+3(2x^3)(9y^2)^{}-27y^3 \\ 8x^9-36x^6y+54x^3y^2-27y^3 \end{gathered}[/tex]So the solution is:
[tex]8x^9-36x^6y+54x^3y^2-27y^3[/tex]I need help with this please thank you very much
So,
We can notice that the graph of g, is translated 2 units to the left and 4 units up. We can express these changes with the following equation:
[tex]g(x)=(x+2)^2+4[/tex]determine whether or not each equation is a linear equation in two variables. if so, identify a b and c a. 2x =5 + yb. y = 5x + 3
Given:
Linear equation in x and y:
An equation of the form y = mx + c or ax + by +c =0 is a linear equation as the degree of both variables x and y is one.
(a) 2x = 5 + y:
The equation can be written as:
[tex]y=2x-5\text{ or 2x-y-5=0}[/tex]This is of the form of ax+by+c=0 so it is linear.
Here, a=2, b= 1, c= - 5
(b) y = 5x + 3:
[tex]y=5x+3\text{ or 5x-y+3=0}[/tex]This is already in the form of ax + by+ c=0 so it also linear.
Here, a= 5 , b = - 1, c= 3
4. What is 10% of 25? Type your answer using numbers only. Your answer
10% = 10/100 = 0.10
therefore:
[tex]25\times0.10=2.5[/tex]answer: 2.5
PLEASE HELP!!!
As part of a major renovation at the beginning of the year, Atiase Pharmaceuticals, Incorporated, sold shelving units (recorded as Equipment) that were 10 years old for $800 cash. The shelves originally cost $6,400 and had been depreciated on a straight-line basis over an estimated useful life of 10 years with an estimated residual value of $400.
2. Prepare the journal entry to record the sale of the shelving units. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field. Do not round intermediate calculations.)
(4 accounts)
Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.
Given,
The selling cost of shelving units that are 10 years old = $800
Original cost of shelving units = $6400
Estimated residual value for 10 years = $400
Assets = Liabilities +Stockholders equity
Calculate the accumulated depreciation for 10 years;-Accumulated depreciation for 10 years=[(Original cost of the equipment-Residual value) / Useful life] ×10 years
=[($6400-$400)/10 years]×10 years
=$600×10 years
=$6000
Calculate book value of equipment.Book value equipment=Original cost of the equipment-Accumulated depreciation for 10 years
=$6400-$6000
=$400
Calculate gain on sale of equipment.
Gain on equipment sale equals selling price minus book value of equipment
=$800-$400
=$400
Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.
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(r^2/s)^3 Simplify this exponential expression
Reason:
When we cube the (r^2) in the numerator, we're multiplying it by itself 3 times
(r^2)^3 = (r^2)*(r^2)*(r^2) = r^(2+2+2) = r^6
or a shortcut is to say
(r^2)^3 = r^(2*3) = r^6
That explains how we get r^6 in the numerator of the final answer.
The s^3 in the denominator is simply the result of cubing the 's' in the original expression.
Answer:
r2x3 / s1x3
Step-by-step explanation:
Raise both the numerator and denominator to the third power. Multiply by the exponents in the numerator (2x3). Multiply the exponents in the denominator (1x3). PF.
use a unit rate to find the unknown value.2/4=?/16the unknown value is?
Let x be the unknown value.
Therefore we have
[tex]\frac{2}{4}=\frac{x}{16}[/tex]So we can inform from the first term that the denominator is double the numerator, since this term is equal to second term with the unknown x, same applies there also.
So,
[tex]\begin{gathered} 2x=16 \\ x=\frac{16}{2}=8 \end{gathered}[/tex]This can be further confirmed by applying cross multiplication,
[tex]\begin{gathered} \frac{2}{4}=\frac{x}{16} \\ 16\times2=4x \\ x=\frac{16\times2}{4}=8 \end{gathered}[/tex]Write a system of equations to describe the situation below, solve using an augmented matrix.The glee club needs to raise money for the spring trip to Europe, so the members are assembling holiday wreaths to sell. Before lunch, they assembled 20 regular wreaths and 16 deluxe wreaths, which used a total of 140 pinecones. After lunch, they assembled 20 regular wreaths and 18 deluxe wreaths, using a total of 150 pinecones. How many pinecones are they putting on each wreath?The regular wreaths each have ? pinecones on them and the large ones each have ? pinecones.
Given
First : They assembled 20 regular wreaths and 16 deluxe wreaths, which used a total of 140 pinecones
Let's represent regular wreaths with r
and
Let's represent deluxe wreaths with d
[tex]20r+16d=140[/tex]Second: They assembled 20 regular wreaths and 18 deluxe wreaths, using a total of 150 pinecones
[tex]20r+18d=150[/tex]We now have
[tex]\begin{gathered} 20r+16d=140\text{ ...Equation 1} \\ 20r+18d=150\text{ ...Equation 2} \end{gathered}[/tex]we can now solve simultaneously, by subtracting the equation 1 and 2
[tex]\begin{gathered} 20r-20r+16d-18d=140-150 \\ -2d=-10 \\ Divide\text{ both sides by -2} \\ -\frac{2d}{-2}=-\frac{10}{-2} \\ \\ d=5 \end{gathered}[/tex]We can subsitute d=5 in equation 1 or 2
[tex]\begin{gathered} 20r+16d=140\text{ ... Equation 1} \\ 20r+16(5)=140 \\ 20r+80=140 \\ 20r=140-80 \\ 20r=60 \\ divide\text{ both sides by 20} \\ \frac{20r}{20}=\frac{60}{20} \\ \\ r=3 \end{gathered}[/tex]The final answer
5 pinecones on the deluxe wreath and 3 pinecones on the regular wreath
State the equations and use the graph to determine where the 2 points intersect
EXPLANATION:
We are given an exponential function as shown below;
[tex]f(x)=2^x[/tex]When shifted one unit right we have the following;
[tex]m(x)=2^{x-1}[/tex]We also are given the quadratic function;
[tex]g(x)=x^2[/tex]When shifted one unit right and one unit up, we would have;
[tex]n(x)=(x-1)^2+1[/tex]The equations for both functions after the transformations would be;
[tex]\begin{gathered} m(x)=2^{x-1} \\ n(x)=(x-1)^2+1 \end{gathered}[/tex]The graphs of both equations is now shown below;
The two points where m(x) and n(x) intersect are;
[tex](1,1)\text{ and }(2,2)[/tex]ANSWER:
[tex]\begin{gathered} (a)\text{ }m(x)=2^{x-1} \\ n(x)=(x-1)^2+1 \\ (b)\text{ }(1,1),(2,2) \end{gathered}[/tex]The value of China's exports of automobiles and parts (in billions of dollars) is approximately f ( x ) = 1.8208 e .3387 x , where x = 0 corresponds to 1998. In what year did/will the exports reach $7.4 billion?
We have the following equation:
[tex]f(x)=108208e^{0.3387x}[/tex]where x denotes the number of years after 1998.
By substituting the given information, we have that
[tex]7.4=1.8208e^{0.3387x}[/tex]and we need to find x. Then, by dividing both sides by 1.8208, we get
[tex]e^{0.3387x=}4.0641475[/tex]then by taking natural logarithm to both sides, we obtain
[tex]0.3387x=ln(4.0641476)[/tex]which gives
[tex]0.3387x=1.4022040[/tex]then, the number of years after 1998 is:
[tex]\begin{gathered} x=\frac{1.4022040}{0.3387} \\ x=4.13996 \end{gathered}[/tex]which means 4 years after 1998. Then, by rounding to the nearest year, the answer is 2002.
what is the distance between two points to the nearest hundredths place?
The formula for calculating the distance between two points is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, for thr given points,
[tex]\begin{gathered} d=\sqrt{(-2-1)^2+(4-3)^2} \\ \text{ = }\sqrt{3+1} \\ \text{ =}\sqrt{4} \\ \text{ =2} \end{gathered}[/tex]what degree are vertical angles?
Vertical angles are opposite angles that also are congruent angles.
Then, due to the given figure, you can conclude that the vertical angles are:
angle FGD and angle of 15° are vertical, then
5x + 3y = 9
can you put it the following equation in slope-intercept form?
[tex]\framebox{Slope intercept: -$\dfrac{5}{3}$x+3}[/tex]
The slope intercept form of [tex]5x+3y=9[/tex] would be written as:
[tex]-\frac{5}{3} x+3[/tex]
A recipe has a ratio of 6 cups of flour to 2 cups ofwater. There is cups of water for each cup offlour.
Given:
A recipe has a ratio of 6 cups of flour to 2 cups of water.
We need to find the number of cups of water for each cups of flour
So, let the number of cups of water = x
We have the following ratio:
[tex]\begin{gathered} \frac{x\text{ cups of water}}{1\text{ cup of flour}}=\frac{2\text{ cups of water}}{6\text{ cups of flour}} \\ \end{gathered}[/tex]Solve for x:
[tex]x=\frac{2}{6}=\frac{1}{3}[/tex]so, the answer will be:
There are 1/3 cups of water for each cup of flour.
What is the x-value of the solution to the system of equations shown below? 2x + y = 20 6x - 5y = 12
Given the equation system:
[tex]\begin{gathered} 1)2x+y=20 \\ 2)6x-5y=12 \end{gathered}[/tex]To solve the system and determine the value of x, first step is to write one of the equations in terms of y:
[tex]\begin{gathered} 2x+y=20 \\ y=20-2x \end{gathered}[/tex]Then replace this expression in the second equation
[tex]\begin{gathered} 6x-5y=12 \\ 6x-5(20-2x)=12 \end{gathered}[/tex]Now that you have an expression with only one unknown, x, you can calculate its value.
Solve the parenthesis using the distributive property of multiplication
[tex]\begin{gathered} 6x-5\cdot20-5\cdot(-2x)=12 \\ 6x-100+10x=12 \\ 6x+10x-100=12 \\ 16x=12+100 \\ 16x=112 \\ \frac{16x}{16}=\frac{112}{16} \\ x=7 \end{gathered}[/tex]