For the polynomial below, -3 and 1 are zeros. Express f (x) as a product of linear factors.
Answers
Explanation
Since -3 and 1 are zeros of the functions, it implies that
[tex](x+3)\text{ }and\text{ }(x-1)[/tex]are factors of the equation.
Therefore we can find the remaining factors below
[tex](x+3)(x-1)=x^2+2x-3[/tex]By long division
[tex]remaining\text{ expression =}\frac{x^4+6x^3+7x^2-8x-6}{x^2+2x-3}=x^2+4x+2[/tex]By quadratic formula
[tex]\begin{gathered} x_{1,2}=\frac{-4\pm\sqrt{4^2-4\times1\times2}}{2\times1} \\ x_1=\frac{-4+2\sqrt{2}}{2},x_2=\frac{-4-2\sqrt{2}}{2} \\ x=-2+\sqrt{2},x=-2-\sqrt{2} \\ therefore \\ (x+2-\sqrt{2})(x+2+\sqrt{2}) \end{gathered}[/tex]The linear factor are
Answer:
[tex]f(x)=(x+3)(x-1)(x+2-\sqrt{2})(x+2+\sqrt{2})[/tex]
Related Questions
a) y=2xb) y=2x+2c) y= -2x + 2d) y=2x - 2
Answers
Answer
Option D is correct.
y = 2x - 2
Explanation
The key to picking the right equation that fits the data in the table is to check each of the options.
Option A
y = 2x
when x = -3,
y = 2x
y = 2(-3)
y = -6
-6 ≠ - 8
Hence, this option is not correct.
Option B
y = 2x + 2
when x = -3,
y = 2x + 2
y = 2(-3) + 2
y = -6 + 2 = -4
-4 ≠ - 8
Hence, this option is not correct.
Option C
y = -2x + 2
when x = -3,
y = -2x + 2
y = -2(-3) + 2 = 6 + 2
y = 8
8 ≠ - 8
Hence, this option is not correct.
Option D
y = 2x - 2
when x = -3
y = 2 (-3) - 2
y = -6 - 2
y = -8
-8 = -8
This is the correct option.
Hope this Helps!!!
Alex’s paycheck was for $624.65. If Alex worked 32.5 hours, what is his rate of pay?
Answers
In order to know the rate of pay, we need to divide the value of the paycheck ($624.65) by the total hours Alex worked (32.5 hours):
$624.65/(32.5 hours) = $624.65/(32.50 hours) = $62465/(3250 hours)
Now, to solve this division, we can do as follows:
Therefore, the rate of pay is
$19.22/hour
Jerry bought a $78 table on sale for 20% off. The best estimate for the discount can be found using which expression? 0.2(80) 0.2170)
Answers
1) Gathering the data
$78 20% off
2) To find the final price Jerry has paid just multiply
78----20%
3) So, the expression used was 78 x (0.8) and Jerry has paid $62.4 for the table
Answer two questions about Equations A and B:Skill SumA. 5 = -2(x - 1)sidesB. 5 = -20 +21) How can we get Equation B from Equation A?Choose 1 answer:a) Rewrite one side (or both) by combining like terms0215b) Rewrite one side for both) using the distributive propertyc) Multiply/divide both sides by the same non-zero constantd) Multiply/divide both sides by the same variable expression Based on the previous answer, are the equations equivalent? In other words,do they have the same solution?
Answers
Rewrite one side(or both) by combining like terms
Explanation:
Equation A: 5 = -2(x - 1)
Equation B: 5 = -20 +2
To get Equation B from Equation A, we equate the right sides of both equations since equating the left side give the same answer.
Left side: 5 = 5
Right side: -2(x - 1) = -20 +2
Then we solve:
-2x + 2 = -18
-2x = -18-2
-2x = -20
x = -20/-2
x = 10
To get Equation B from Equation A, we make x = 10
Rewrite one side(or both) by combining like terms
There are 130 people at a meeting. Theyeach give a Valentine's Day card toeveryone else. How many cards weregiven?
Answers
Permutations
Suppose there are only two people in the meeting. Person A gives a card to person B and vice-versa. Two cards were given.
Now we have 3 people. Person A gives two cards. Person B gives two cards. Person C gives two cards. Total = 6 cards given.
Each people gives a card to everyone else (except themselves, of course) and it's done by everyone in the meeting, thus for 130 people:
130 x 129 = 16,770 cards were given
Help me with this math and explaining the question solution and quickly and explain it
Answers
To find the distance between V1 and the aquarium we can use the formula of the distance between two points in the plane, that is,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where }(x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points} \end{gathered}[/tex]So, in this case, we have
[tex]\begin{gathered} V1(-6,5) \\ AQ(5,5) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(5-(-6))^2+(5-5)^2} \\ d=\sqrt[]{(5+6)^2+(5-5)^2} \\ d=\sqrt[]{(11)^2+(0)^2} \\ d=\sqrt[]{(11)^2} \\ d=11 \end{gathered}[/tex]Therefore, the distance between v1 and the aquarium is 11 units.
find an equation of the tangent line to the graph of the function at the given point,use a graphing utility to graph the function and its tangent line at the point, anduse the tangent feature of a graphing utility to confirm your results.
Answers
The equation of the tangent line may be identified using the first derivative of the function which gives us its slope.
[tex]\begin{gathered} y=\cos3x \\ \\ y^{\prime}=-3\sin3x \\ \\ m=-3\sin3x \\ \\ m=-3\sin3(\frac{\pi}{4}) \\ \\ m=-3(\frac{\sqrt{2}}{2}) \\ \\ m=-\frac{3\sqrt{2}}{2} \end{gathered}[/tex]The tangent line passes through (/4, -√2/2) so we can solve for the y-intercept, b.
[tex]\begin{gathered} y=mx+b \\ \\ -\frac{\sqrt{2}}{2}=-\frac{3\sqrt{2}}{2}(\frac{\pi}{4})+b \\ \\ -\frac{\sqrt{2}}{2}=-\frac{3\pi\sqrt{2}}{8}+b \\ \\ b=-\frac{\sqrt{2}}{2}+\frac{3\pi\sqrt{2}}{8} \\ \\ b=\frac{-4\sqrt{2}}{8}+\frac{3\pi\sqrt{2}}{8} \\ \\ b=\frac{(3\pi-4)\sqrt{2}}{8} \end{gathered}[/tex]So the equation of the tangent line is:
[tex]y=-\frac{3\sqrt{2}}{2}x+\frac{(3\pi-4)\sqrt{2}}{8}[/tex]the length of one leg of a right triangle is 15 m. The length of the other leg is 9 m shorter than the length of the hypotenuse. Find the length of the hypotenuse.
Answers
Let the hypotenuse is x
The length of the other leg is 9 m shorter than the length of the hypotenuse
The length of second leg = Hypotenuse - 9
The length of second leg = x - 9
the length of one leg of a right triangle is 15 m.
The first leg = 15m
Pythagoras Theorem : In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
Apply pythagoras for the value of x :
[tex]\begin{gathered} \text{ Hypotenuse}^2=Base^2+Perpendicular^2 \\ x^2=15^2+(x-9)^2 \\ x^2=225+x^2+81-18x \\ x^2-x^2=225+81-18x \\ 18x=306 \\ x=\frac{306}{18} \\ x=17 \end{gathered}[/tex]as x represent the hypotnuese, SO
Hypotenuse = 17m
A truck averages 16 miles per yulion and has a 25 gallon gas tank. What is the furthest distance the truck can travel without stopping for gas?
Answers
A truck averages 16 miles per gallon and has a 25 gallon gas tank. What is the furthest distance the truck can travel without stopping for gas?
Apply proportion
16/1=x/25
solve for x
x=16*25
x=400 miles
answer is 400 milesWhat is the distance between the points (-9, 4) and (3,-12)? A 12 units B. 16 units c. 20 units D. 28 units
Answers
Answer:
C
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 9, 4 ) and (x₂, y₂ ) = (3, - 12 )
d = [tex]\sqrt{(3-(-9))^2+(-12-4)^2}[/tex]
= [tex]\sqrt{(3+9)^2+(-16)^2}[/tex]
= [tex]\sqrt{12^2+256}[/tex]
= [tex]\sqrt{144+256}[/tex]
= [tex]\sqrt{400}[/tex]
= 20 units
Math help with problems Is this line linear or nonlinear
Answers
Answer:
[tex]It\text{ is linear}[/tex]Explanation:
Here, we want to check if the given line is linear or not
From the image shown, the line connects two points on the axes
This connection is in the form of a line segment
Thus, we can confirm that the line is linear
1) 42,58, 67,55, 40, 69, 66, 51, 46, 48, 68 Minimum : Q: Q2: Q, Maximum :
Answers
EXPLANATION
Minimum
The first Quartile is the value separating the lower quarter and higher three - quarters of the data set.
The first quartile is computed by taking the median of the lower half of a sorted set.
Arranging terms in ascending order
40, 42 , 46, 48, 51, 55, 58, 66, 67, 68, 69
Here, we can see that:
Minimum = 40
Maximum = 69
Q2=55 (median)
Taking the lower half of the ascending set:
Counting the number of terms in the data set:
{40, 42 , 46, 48, 51, 55, 58, 66, 67, 68, 69}
{1, 2 , 3, 4, 5, 6, 7, 8, 9, 10, 11}
The number of terms in the data set is:
11
Since the number of terms is odd, take the elements below the middle one, that is, the lower 5 elements.
40, 42 , 46, 48, 51
Median of 40, 42 , 46, 48, 51:
The number of terms in the data set is 5.
Since the number of terms is odd, the median is the middle element of the sorted set.
Q1: 46
------------------------------------
Q3:
Since the number of terms is odd, take the elements above the middle one, that is, the upper 5 elements.
58, 66, 67, 68, 69
The number of terms in the data set is
5
Since the number of terms is odd, the median is the middle element of the sorted set.
Q3=67
------------------------------------------------------------------------------------
Interquartile Range:
The interquartile range is the difference of the first and third quartiles
We have that:
Q1=46
Q3=67
Computing the difference between 67 and 46:
67-46= 21
Interquartile Range=21
-------------------------------
Answers:
Minimum = 40
Q1=46
Q2=55 (median)
Q3=67
Maximum = 69
Interquartile Range=21
hello I'm having some difficulty on this question thank you for viewing it and helping me
Answers
The simple interest charged by the lender on Alonzo is $ 126 and the amount paid after 6 years is $ 826.
Principal amount of loan = $ 700
Time period = 6 years
Interest rate = 3 %
The simple interest is charged by the lender:
The interest will be:
SI = p × r × t / 100
Substitute the values, we get that:
SI = 700 × 3 × 6 / 100
SI = 7 × 3 × 6
SI = $ 126
The amount paid by Alonzo after 6 years will be:
Amount = $ 700 + $ 126
A = $ 826
Therefore, the simple interest charged by the lender on Alonzo is $ 126 and the amount paid after 6 years is $ 826.
Learn more about simple interest here:
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_____ ______ ______says that people are able to decide what to buy and how much they are willing and able to pay depending on the satisfaction they receive from the service/product.
Answers
Decision makers say that people can decide what to buy and how much they are willing and able to pay depending on the satisfaction they receive from the service/product.
What is meant by decision maker?A decision maker is a person or group in charge of making crucial strategic decisions based on a variety of factors, such as the amount of time available, the resources at hand, the type and quality of information at hand, and the number of interested parties.
According to those who make decisions, consumers can choose what they want to buy and how much they are willing and able to pay based on how satisfied they are with the service or product.
Making decisions is crucial because it allows you to select from a variety of options. It is important to gather all available information and consider the advantages and disadvantages of it before making a decision. It is imperative to concentrate on actions that can assist in making the best decisions.
To learn more about decision maker refer to:
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Find the slope of each.1. (0, 4) and (2, -3)
Answers
Answer:
slope = -3.5
Explanation:
The points we have are:
[tex]\begin{gathered} (0,4) \\ (2,-3) \end{gathered}[/tex]We have to label the coordinates as follows:
[tex]\begin{gathered} x_1=0 \\ y_1=4 \\ x_2=2 \\ y_2=-3 \end{gathered}[/tex]And now we use the formula to calculate the slope between the points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We substitute the known values:
[tex]m=\frac{-3-4}{2-0}[/tex]And solve the operations to find the slope "m" between the points:
[tex]\begin{gathered} m=\frac{-7}{2} \\ m=-3.5 \end{gathered}[/tex]Answer: slope = -3.5
2(x+9)=2x+18What is the Name of the property listed above -commutative property of addition-commutative property of multiplication -Associative property of addition -Associative property of multiplication -Distributive property -additive identity -Multiplication identity -Zero property of multiplication-Multiplication property of -1 -none of the above.
Answers
Distributive property
Explanation:Given:
[tex]2(x+9)\text{ = 2x + 18}[/tex]To find:
the name of the property stated
[tex]\begin{gathered} 2(x\text{ + 9\rparen = 2\lparen x\rparen + 2\lparen9\rparen} \\ \\ The\text{ form above is the same as:} \\ a(b\text{ + c\rparen = }a(b)\text{ + a\lparen c\rparen} \\ This\text{ is known as distributive property.} \end{gathered}[/tex][tex]\begin{gathered} 2(x)\text{ + 2\lparen9\rparen = 2x + 18} \\ \\ Hence,\text{ 2\lparen x + 9\rparen = 2x + 18 is a distributive property} \end{gathered}[/tex]A candy store sells different sized bags of jelly beans. The line plot shows the welghts of ten bags. Weight of Jelly Bean Bags X XXXala x X+CO i colwt inloo - 50 1 Pounds Mikalya bought all of the bags weighing less than 2 pound. How many pounds of jelly beans did Mikalya buy? OA pound pound OB. is pound pound
Answers
bags less than 3/8
[tex]\begin{gathered} \frac{1}{4}\longrightarrow2 \\ \\ \frac{1}{8}\longrightarrow1 \end{gathered}[/tex]are 3
to fin the total pounds we multiply each weight by the number of bags
[tex]\begin{gathered} \frac{1}{4}\times2=\frac{1}{2} \\ \\ \frac{1}{8}\times1=\frac{1}{8} \end{gathered}[/tex]now sum
[tex]\begin{gathered} \frac{1}{2}+\frac{1}{8} \\ \\ \frac{(8\times1)+(2\times1)}{8\times2} \\ \\ \frac{8+2}{16} \\ \\ \frac{10}{16}=\frac{5}{8} \end{gathered}[/tex]total weight is 5/8pounds
ESFind the distance d(P. P2) between the points P, and P2-omennsP. = (-4.3)P2 = (3.2)ERE!(P, P2) =O(Simplify your answer. Type an exact answer using radicals as needed.)1 Guit2 Gunents
Answers
We have two points and we need to calculate the distance between them.
The points are P1(-4,3) and P2(3,2).
We can apply the following formula for the distance between points:
[tex]D=\sqrt{(x_2-x_1)^2}+(y_2-y_1)^2[/tex][tex]\begin{gathered} D=\sqrt{(3-(-4))^2}+(3-2)^2 \\ D=\sqrt{7^2+1^2}=\sqrt{49+1}=\sqrt{50}=\sqrt{(25\cdot2})=5\sqrt{2} \end{gathered}[/tex]The answe is 5 times the square root of 2:
[tex]D=5\sqrt{2}[/tex]Identify the term that completes the equation. XZ2=(WZ) (?)Please help
Answers
Given triangles, XZW and XZY are right-angle triangles.
Using the Pythagorean theorem for XZW, we get
[tex]XZ^2+WZ^2=WX^2[/tex]Using the Pythagorean theorem for XZY, we get
[tex]XZ^2+XY^2=ZY^2[/tex][tex]XZ^2=ZY^2-XY^2[/tex]Using the Pythagorean theorem for WXY, we get
[tex]WX^2+XY^2=WY^2[/tex][tex]undefined[/tex]how to answer this system of equations using cramer's rule
Answers
Given:
Given the system of equations:
[tex]\begin{gathered} c+w+p=456 \\ c-p=80 \\ p=2w-2 \end{gathered}[/tex]Required: Solution of the system using Cramer's rule
Explanation:
The system of equations can be rewritten as
[tex]\begin{gathered} c+p+w=456 \\ c-p+0w=80 \\ 0c+p-2w=-2 \end{gathered}[/tex]Write down the augmented matrix.
[tex]\begin{bmatrix}{1} & {1} & {1} & {456} \\ {1} & {-1} & {0} & {80} \\ {0} & {1} & {-2} & {-2} \\ {} & {} & {} & {}\end{bmatrix}[/tex]Calculate the main determinant.
[tex]\begin{gathered} D=\det\begin{bmatrix}{1} & {1} & {1} \\ {1} & {-1} & {0} \\ {0} & {1} & {-2}\end{bmatrix} \\ =1\left(2-0\right)-1\left(-2-1\right) \\ =2+3 \\ =5 \end{gathered}[/tex]Substitute the c-column with RHS and find the determinant.
[tex]\begin{gathered} D_c=\det\begin{bmatrix}{456} & {1} & {1} \\ {80} & {-1} & {0} \\ {-2} & {1} & {-2}\end{bmatrix} \\ =456\left(2-0\right)-80\left(-2-1\right)-2\left(0+1\right) \\ =912+240-2=1150 \end{gathered}[/tex]Substitute the p-column with RHS and find the determinant.
[tex]\begin{gathered} D_p=\det\begin{bmatrix}{1} & {456} & {1} \\ {1} & {80} & {0} \\ {0} & {-2} & {-2}\end{bmatrix} \\ =1(-160-0)-1(-912+2) \\ =-160+910 \\ =750 \end{gathered}[/tex]Substitute the w-column with RHS and find the determinant.
[tex]undefined[/tex]Identify the vertex and sketch the graph.f (x) = -2x 2 - 24x - 72
Answers
ANSWER
Vertex = (-6, 0) Option B
Graph:
EXPLANATION
Given:
[tex]f(x)=-2x^2-24x-72[/tex]Desired Outcome:
Vertex and graph
Rewrite the equation in vertex form
[tex]y=a(x-h)^2+k[/tex]where:
(h, k) is the vertex.
Now, determine the vertex of the equation
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-24)}{2(-2)} \\ h=\frac{24}{-4} \\ h=-6 \end{gathered}[/tex][tex]k=-\frac{D}{4a}[/tex]Let's determine the value of D
[tex]\begin{gathered} D=b^2-4ac \\ D=(-24)^2-4(-2)(-72) \\ D=576-576 \\ D=0 \end{gathered}[/tex]Now,
[tex]\begin{gathered} k=-\frac{D}{4a} \\ k=-\frac{0}{4(-2)} \\ k=\frac{0}{8} \\ k=0 \end{gathered}[/tex]Therefore, the vertex (h, k) = (-6, 0) and when we plot this on a graph, we have:
Hence, the correct option is B.
The temperature of a solution in a science experiment is -6.2°C. Jesse wants to raise the temperature so that it is positive. (a) Give an example of a number of degrees Celsius by which Jesse could raise the temperature. (b) Write a equation to represent the solution.
Answers
Hello!
First, the temperature is -6.2ºC, and Jesse wants to raise it until be positive.
(a) Give an example of a number of degrees Celsius by which Jesse could raise the temperature.If we add 6.2ºC, we will obtain a temperature equal to 0ºC, right? So, to the temperature be positive you can choose any temperature greater than 6.2º.
For example, I'll choose 15ºC.
(b) Write an equation to represent the solution. We will write the current temperature plus the temperature that we will add, then we obtain the new temperature, look:
-6.2ºC + 15ºC = 8.8ºC
A sales person is given a choice of two salary plans. Plan 1 is weekly salary of $600 plus 2 percent commission of sales. Plan 2 is a straight commission of 10% of sales. How much in sales must he make in a week for both plans to result in the same salary?
Answers
Answer:
He must make $7,500 in sale
Step-by-step explanation:
Let's say:
s = amount make in sales per week
P1 = weekly salary of Plan 1
P2 = weekly salary of Plan 2
P1 and P2 can be expressed using the fixed amount plus the commission.
P1 = 600 + 0.02s
P2 = 0 + 0.1s
P2 = 0.1s
If both plans result in the same salary:
P1 = P2
600 + 0.02s = 0.1s
0.1s - 0.02s = 600
0.08s = 600
s = 600/0.08
s = $7,500
Which equation does the following grid represent? X X XX X XX X X XX X X XX X X A 0.92 - 0.19 = 0.73 OB. 0.73 +0.19 = 0.92 O C. 1.00 - 0.19 = 0.81 O D. 1.00 +0.73 = 1.73
Answers
In the Diagram,
We have a box
Total squares: 100
In Red we have= 92 squares
The blank squares= 8
"X" squares = 19
2) Then, Dividing each by 100:
0.92 red -0.19x =0.73 the amount of red squares not marked with an x
use the point slope formula in the given points to choose the correct linear equation in slope intercept formfor ( 4,-3) and (-2,5)
Answers
The point-slope formula is
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope of a line passing through the point (x₁, y₁).
Also, the slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this problem, the line passes through points (4, -3) and (-2, 5). Thus, we have:
x₁ = 4
y₁ = -3
x₂ = -2
y₂ = 5
Then, the slope is
[tex]m=\frac{5-(-3)}{-2-4}=\frac{5+3}{-6}=\frac{8}{-6}=-\frac{4}{3}[/tex]And the equation in point-slope form is
[tex]y-(-3)=-\frac{4}{3}(x-4)[/tex]Now, we need to rewrite this equation in slope-intercept form. The slope-intercept equation of a line with slope m and y-intercept b is
[tex]y=mx+b[/tex]Thus, we need to isolate y on the left side of the equation to obtain the slope-intercept form, as follows:
[tex]\begin{gathered} y+3=-\frac{4}{3}x-\frac{4}{3}(-4)\text{ using the distributive property of multiplication over addition} \\ \\ y+3=-\frac{4}{3}x+\frac{16}{3} \\ \\ y+3-3=-\frac{4}{3}x+\frac{16}{3}-3 \\ \\ y=-\frac{4}{3}x+\frac{16}{3}-\frac{9}{3} \\ \\ y=-\frac{4}{3}x+\frac{7}{3} \end{gathered}[/tex]Therefore, the slope-intercept form of that linear equation is
[tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]A punter kicks a football. Its height (h) in meters, t seconds after the kick is givenby the equation: h(t) = -4.912t^2 +18.24t +0.8. The height of an approaching blocker'shands is modeled by the equation: g(t) = -1.43t+4.26, using the same time. Can theblocker knock down the punt? If so, at what time does this happen?
Answers
The figure below shows a juice box in the shape for a rectangular prism
Answers
(a)
Given the dimensions of the rectangular prism l = 7 cm, w = 2 cm, h = 8 cm, the surface area of a rectangular prism can be computed using the equation
[tex]SA=2(wl+hl+hw)[/tex]Substitute the values on the equation above and compute, we get
[tex]SA=2\lbrack(2cm\times7cm)+(8cm\times7cm)+(8cm\times2cm)\rbrack=172cm^2[/tex]The volume of the rectangular prism can be computed using the equation
[tex]V=l\times w\times h[/tex]Plug in the values on the equation above and compute, we get
[tex]V=(7cm)\times(2cm)\times(8cm)=112cm^3[/tex](b) For the amount of juice inside the rectangular prism, we will use volume.
(c) For the amount of coating of wax for the box, we will use surface area.
Write the equation of the line in standard form that passes through point P(-5,7) andPerpendicular to the equation of the line y=-x+2.
Answers
The given equation is
[tex]y=-x+2[/tex]We have to find a new line perpendicular to the given line and must pass through P(-5,7).
First, we use the definition of perpendicularity for two lines.
[tex]m_1\cdot m_2=-1[/tex]Where one of the slopes is equal to -1 because the coefficient of x in the given equation is -1. Let's find the other slope.
[tex]\begin{gathered} m\cdot(-1)=-1 \\ m=1 \end{gathered}[/tex]This means the new perpendicular line has a slope of 1.
Now, we use the slope we found, the point P, and the point-slope formula, to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-7=1(x-(-5)) \\ y-7=x+5 \\ y=x+5+7 \\ y=x+12 \end{gathered}[/tex]Therefore, the equation of the new perpendicular line is y = x + 12.I need help with this math question I already solved the first question but I don't understand the second.
Answers
We can solve this question using cross multiplication,
If the number of students who sleep 6 hours a day increases by, this means we'll have a total of 6 students who sleep 6 hours a day.
We want the ratio to be same: 15%
Then we can write:
[tex]\frac{6}{N}=\frac{15\%}{100\%}[/tex]6 students are the 15%, then N students are the 100%
Now solve for N:
[tex]\begin{gathered} 6·100=15·N \\ \end{gathered}[/tex][tex]N=\frac{600}{15}[/tex][tex]N=40[/tex]The answer is 40 students are expected.
This is a reasonable answer, given that if the number of students who sleep 6 hours doubles, for the rate to remain the same, the total of students must double.
which of the following is the solution of the system of equations below? 6x+6y=-6 5x+y=-13
Answers
First, we divide the first equation by -6
[tex]\begin{gathered} 6x+6y=-6 \\ -x-y=1 \end{gathered}[/tex]Then, we combine this equation with the second one
[tex]\begin{gathered} 5x-x+y-y=1-13 \\ 4x=-12 \\ x=-\frac{12}{4} \\ x=-3 \end{gathered}[/tex]Now, we use the x-value to find y
[tex]\begin{gathered} 5x+y=-13 \\ 5(-3)+y=-13 \\ -15+y=-13 \\ y=-13+15 \\ y=2 \end{gathered}[/tex]Hence, the solution to the system is (-3, 2).