Answers
step 1
Find the slope
we take the points
(0,7) and (1,15)
m=(15-7)/(1-0)
m=8/1
m=8
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=8
b=7 -------> (0,7) is the y-intercept
substitute
y=8x+7Related Questions
what is the distance between two points to the nearest hundredths place?
Answers
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]Frustratingly this is the third time I’m asking this question that two tutors got wrong. Please help?
Answers
To answer this question, we need to translate each of the expressions into algebraic form. Then we have:
1. We have that one number is 2 less than a second number.
In this case, let x be one of the numbers, and y the second number. Now, we can write the expression as follows:
[tex]x=y-2[/tex]2. We also have that twice the second number is 2 less than 3 times the first:
[tex]2y=3x-2[/tex]3. And now, we have the following system of equations:
[tex]\begin{cases}x=y-2 \\ 2y=3x-2\end{cases}[/tex]4. And we can solve by substitution as follows:
[tex]\begin{gathered} x=y-2\text{ then we have:} \\ \\ 2y=3(y-2)-2 \\ \\ 2y=3(y)+(3)(-2)-2 \\ \\ 2y=3y-6-2 \\ \\ 2y=3y-8 \end{gathered}[/tex]5. To solve this equation, we can subtract 2y from both sides, and add 8 from both sides too:
[tex]\begin{gathered} 2y-2y=3y-2y-8 \\ 0=y-8 \\ 8=y-8+8 \\ 8=y \\ y=8 \end{gathered}[/tex]6. Since y = 8, then we can use one of the original equations to find x as follows:
[tex]\begin{gathered} x=y-2\Rightarrow y=8 \\ x=8-2 \\ x=6 \end{gathered}[/tex]Therefore, we have that both numbers are x = 6, and y = 8.
In summary, we have that:
• The smaller number is 6.
,• The larger number is 8.
State the equations and use the graph to determine where the 2 points intersect
Answers
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]What is the value of xin the product of powers below? 6^9 * 6^x = 6^2 -11 -7 7 11
Answers
Given:
[tex]6^{9\text{ }}\ast6^x=6^2[/tex]To find the value of x, first apply exponential property which is:
[tex]a^m\text{ }\ast a^{n\text{ }}=a^{m+n}[/tex]Now we have:
[tex]6^{9+x\text{ }}=6^2[/tex]Since both bases are equal, let's remove both bases, take the exponent and find x:
[tex]9\text{ + x = 2}[/tex]Now subtract from both sides:
[tex]9\text{ - 9 + x = 2 - }9[/tex][tex]0\text{ + x }=\text{ -7}[/tex][tex]x\text{ = -7}[/tex]The value of x is -7
I need help with the calculus portion of my ACT prep guide
Answers
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]The water trough shown in the figure to the right is constructed with semicircular ends. Calculate its volume in gallons if thediameter of the end is 19 in. and the length of the trough is 5 ft. (Hint: Be careful of units.)(Round to the nearest tenth as needed.)
Answers
Solution
For this case we can use the following formula:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]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
Answers
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
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
Answers
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
what would be the most appropriate domain for this function? Number 7
Answers
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...}
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.
Answers
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
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)
Answers
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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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)
Answers
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]
A sequence is generated by An= -2n - 4, find the 5 terms of the sequence
Answers
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
what degree are vertical angles?
Answers
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
A recipe has a ratio of 6 cups of flour to 2 cups ofwater. There is cups of water for each cup offlour.
Answers
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 value of x makes this equation true?3 - 2x = 8 - 13
Answers
First we have to solve the substraction on the right side of the equation:
[tex]3-2x=-5[/tex]Now we add 2x on both sides:
[tex]\begin{gathered} 3-2x+2x=-5+2x \\ 3=-5+2x \end{gathered}[/tex]Now add 5 on both sides:
[tex]\begin{gathered} 3+5=-5+5+2x \\ 8=2x \end{gathered}[/tex]And divide both sides by 2:
[tex]\begin{gathered} \frac{8}{2}=\frac{2x}{2} \\ 4=x \end{gathered}[/tex]The value of x that makes the equation true is 4
identify the maximum from the tabletype your answer as an ordered pair (x,y)
Answers
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
I have to find the least common denominator and the domain, but i’m lost
Answers
Explanation:
[tex]\frac{2x\text{ - 3}}{x^2+6x+8}\text{ + }\frac{10}{x^2+x\text{ - 12}}[/tex]Finding the LCM:
[tex]\begin{gathered} =\frac{(2x-3)(x^2+x-12)+10(x^2+6x+8)}{(x^2+6x+8)(x^2+x-12)} \\ =\frac{(2x)(x^2+x-12)-3(x^2+x-12)+10(x^2+6x+8)}{(x^2+6x+8)(x^2+x-12)} \\ =\frac{(2x^3+2x^2-24x)-3x^2-3x+36+10x^2+60x+80}{(x^2+6x+8)(x^2+x-12)} \end{gathered}[/tex][tex]undefined[/tex]Can you please help me out with a question
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Using the figure, determine the length, in units, of LM
Answers
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
5 1/8 divided by 10
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
Answers
If [tex]5\frac{1}{8}[/tex] is divided by 10, 41/80 is the quotient.
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line.
The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.
The given expressions are
[tex]5\frac{1}{8}[/tex] / 10
41/ 8 ÷10
= 41/8 × 1/10
= 41/80
This is the quotient.
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I find an awesome pair of red Jimmy Choo ‘Romy 100’ heels for 35% off. If the sale price is $812.50, what was the original price before the markdown?
Answers
812.50 ------------------------ 65%
x ----------------------- 100%
x = (100 x 812.50) / 65
x = 81250 / 65
x = $1250
The original price was $1250.00
Find the equation of a line perpendicular to y + 1 =-1/2xthat passesthrough the point (-8, 7).
Answers
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+23The 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!
Answers
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
which is higher? -32 or 36?
Answers
36 is higher
positive numbers are higher than negative numbers
Hence 36 is higher than -32
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
Answers
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
I got the top part of my homework right, I’m just not sure how to do the bottom one. Thank you!
Answers
The graph of a function and its inverse are always symmetrical across the line defined by:
[tex]y=x[/tex]This is true for any function and its inverse.
solve by substitution x+2y-z = 4 3x – y +z = 5 2x + 3y + 2z = 7
Answers
You have the following system of equations:
Use a unit multiplier to convert 90 meters per minute to meters per second.
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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.
(r^2/s)^3 Simplify this exponential expression
Answers
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.