The linear equation that is perpendicular to the line x+3y=21 is:
y = 3*x - 6
How to find the equation of the line?A general line in the slope-intercept form is written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two linear equations are perpendicular if the product between the two slopes is equal to -1.
Rewriting the given line we can get:
x +3y = 21
3y = 21 - x
y = 21/3 - x/3
y = (-1/3)*x + 21/3
Then the slope is (-1/3), if our line is perpendicular to this one, then:
m*(-1/3) = -1
m = 3
our line is:
y = 3*x + b
To find the value of b, we use the fact that our line passes through (1, - 3)
-3 = 3*1 + b
-3 - 3 = b
-6 = b
The line is y = 3*x - 6
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Line L passes through point (10,−1) and line P is the graph of 5x−7y=8.
If L⊥P , what is the equation of L?
The equation of line L is [tex]7x+5y=70[/tex].
Given,
Line L passes through point (10,-1)
Equation of line P = [tex]5x-7y=8[/tex]
Line L is perpendicular to line P
First find the slope of line P, for that convert the equation into the general form [tex]y=mx+c[/tex]
Where, m=slope
[tex]5x-7y=8\\\\5x-8=7y\\\\y=\frac{5}{7}x-\frac{8}{7}[/tex]
Comparing with general form,
[tex]m=\frac{5}{7}[/tex]
Any line perpendicular to it should have slope in the form [tex]-\frac{1}{m}[/tex]
So, the slope of line L becomes [tex]-\frac{7}{5}[/tex]
Equation of line L can be written as [tex]y-y1=m(x-x1)[/tex]
Where, (x1,y1) is the point through which line passes and 'm' is the slope of line L
[tex]y-(-1)=-\frac{7}{5}(x-10)\\\\5(y+1)=-7x+70\\\\5y+5=-7x+70\\\\7x+5y=70[/tex]
Thus, the equation of line L is [tex]7x+5y=70[/tex]
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numbers 14. and 15. pls really need it
Answer:
Step-by-step explanation:
for 15 115 hours befor
A larger pipe fills a water tank twice as fast as a smaller pipe. When both pipes are used, they fill the tank in 55 hours. If the larger pipe is left off, then how long would it take the smaller pipe to fill the tank?
For this exercise you need to use the Work-rate formula. This is:
[tex]\frac{t}{t_A}+\frac{t}{t_B}=1[/tex]Where:
- "t" is the time for the objects A and B together.
- The individual time for object A is:
[tex]t_A[/tex]- The individual time for object B is:
[tex]t_B[/tex]In this case, you can idenfity that:
[tex]\begin{gathered} t=55 \\ t_A=2t_B \\ _{} \end{gathered}[/tex]Substitute them into the formula:
[tex]\frac{55}{2t_B_{}_{}}+\frac{55}{t_B}=1[/tex]Now you must solve for:
[tex]t_B[/tex]You get that this is:
[tex]\begin{gathered} \frac{55+2(55)}{2t_B}=1 \\ \\ \frac{55+110}{2t_B}=1 \\ 165=(1)(2t_B) \\ \\ \frac{165}{2}=t_B_{} \\ \\ t_B=82.5 \end{gathered}[/tex]The answer is: It takes the smaller pipe 82.5 hours to fill the tank.
A design was constructed by using two rectangles, ABCD and A'B'C'D'. RectangleA'B'C'D' is the result of a translation of rectangle ABCD. The table of translations isshown below. Find the coordinates of point B.
From the table, to transform points in rectangle ABCD into A'B'C'D', we have to apply the next rule: (x, y) → (x+1, y-3). That is,
A(2, 4) → (2+1, 4-3) → A'(3, 1)
C(2, -1) → (2+1, -1-3) → C'(3, -4)
D(-6, -1) → (-6+1, -1-3) → D'(-5, -4)
Then, if we want to transform a point in A'B'C'D', the rule is: (x,y) → (x-1, y+3). Applying this rule to point B', we get:
B'(-5, 1) → (-5-1, 1+3) → B(-6, 4)
GHA PBDCIdentify the apothem (a), the radius (r), and the perimeter (p) of the regular figure.A. a=OB,r=OP.P = (8)ABB. a= OP,r=OA.P = ABC. a=OP,r=OBP = PBD. a=OP,r=OA. P = (8)AB
Step 1
Given;
Step 2
The apothem is a perpendicular line from the center of a regular polygon to one of the sides. O is the center of the regular polygon.
The radius of a regular polygon is a segment with one endpoint at the center and the other endpoint at one of the vertices. Thus, there are n radii in an n-sided regular polygon. The center and radius of a regular polygon are the same as the center and radius of a circle circumscribed about that regular polygon.
The perimeter of a regular polygon is a sum of the length of all the sides of the polygon.
Thus, the required parts are;
[tex]a=OP,\text{ r=OA, p=8AB}[/tex]Answer; Option D
cuanto es 4/10+5/10
Usa la siguiente propiedad:
[tex]\begin{gathered} \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c} \\ \frac{4}{10}+\frac{5}{10}=\frac{4+5}{10}=\frac{9}{10}=0.9 \end{gathered}[/tex][tex]\frac{3}{5}+\frac{6}{5}=\frac{3+6}{5}=\frac{9}{5}=1.8[/tex]72 less than the quotient of a number and -2 is -88Select all the statements that are true about the sentence shown.A.) The equation representing this sentence is 72 - x/-2 = -88 because x/-2 is subtracted from 72.B.) The solution to the equation -40 + x = -8 is equal to the unknown number in the sentenceC.) The solution is 32 because -88 + 72 = -16 and -16 times -2 = 32.D.) The solution to the equation -56 + 8x = 200 is equal to the unknown number in the sentence.
ANSWER
C.) The solution is 32 because -88 + 72 = -16 and -16 times -2 = 32.
EXPLANATION
We have that 72 less than the quotient of a number and -2 is 88.
First, let us write the equation from the sentence above.
Let the number be x.
The quotient of x and -2 means x/-2
If we subtract 72 from that quotient, the answer is -88.
Therefore, the sentence is:
[tex]\frac{x}{-2}\text{ - 72 = -88}[/tex]A cannot be correct because the equation is wrong.
B cannot be correct because the equation does not relate to the sentence given.
C is correct because if we solve for x from the equation, we get 32.
That is:
x/-2 = -88 + 72
x/-2 = -16
Multiply through by -2:
x = -16 * -2
x = 32
D cannot be correct because the equation does not relate to the sentence given.
The only correct option is C.
Hi I am having trouble with solving and finding the answers to this problem Find the perimeter of the figure. Use 3.14 for ππ and round to at least 1 decimal place.
Given:-
An reatacngle with a half sphere at one side.
To find:-
The perimeter of the given image.
Now we are going to find the perimeter of the half sphere. The formula to find half sphere is,
[tex]\pi r+d[/tex]Where r is radius and d is diameter.
The radius of the sphere is 2.5 and the diameter is 5. Substituing the values we get,
[tex]\begin{gathered} \pi r+d=3.14\times2.5+5 \\ \text{ =12.85} \\ \text{ =12.9} \end{gathered}[/tex]Now we find the perimeter of the rectangle below. we get,
[tex]5+5+5=15_{}[/tex]Now to get the total perimeter we need to add both the values. so we get,
[tex]12.9+15=27.9[/tex]So the required perimeter is 27.9
5. The locations of Andy's housc, school and local park form a triangle, as shown. School 4 miles House ? 12 miles Park Which is a possible distance from the local park to Andy's school? A. 4 miles B. 8 miles C. 10 miles D. 16 miles
Firestone tires cost $50.20 each. A set of four Lemans tires costs $197.99. How much can a person save by buying the set of four Lemans tires compared to four Firestone tires?
Answer:
591.16
Step-by-step explanation:
im pretty sure this is right
At State College last term, 61 of the students in a Physics course earned As, 89 earned Bs, 119 got Cs, 79 were issued Ds, and 70 failed the course. If this grade distribution was graphed on a pie chart, how many degrees would be used to indicate the A region? Round your answer to the nearest whole degree.
The number of degrees that would be used to indicate region A is 53°
EXPLANATION
Number of students with As = 61
Number of students with Bs = 89
Number of students with Cs =119
Number of students with Ds = 79
Number of students with F = 70
To find the number degrees that would be used to indicate A region, we will use the formula below:
[tex]\text{ Region A in degre}e=\frac{Number\text{ of As}}{\text{Total number of student}}\times360^o[/tex]Number of As = 61
Total number of students = 61 + 89 + 119 + 79 + 70 = 418
Substitute the values into the formula and evaluate.
[tex]A\text{ region in degre}e=\frac{61}{418}\times360^o[/tex][tex]=52.55885[/tex][tex]\approx53^o\text{ to the nearest degre}e[/tex]Therefore, the number of degrees ithat would be used to indicate region A is 53°
Find the slope of the line that passes through each pair of points. (4,3) and (-6-5)
Answer:
4/5
Explanation:
Given the points (4,3) and (-6,-5), the slope of the line that passes through the two points is:
[tex]\begin{gathered} Slope=\frac{Change\text{ in y}}{\text{Change in x}} \\ =\frac{-5-3}{-6-4} \\ =\frac{-8}{-10} \\ =\frac{4}{5} \end{gathered}[/tex]The slope of the line is 4/5.
2. Lisa owns 40% of the stock in a private catering corporation.There are 1,200 shares in the entire corporation.How many shares does Lisa own?
To find the umber of shares Lisa owns we need to calculate how many shares 40 % represents from the total 1,200 shares.
[tex]\begin{gathered} \frac{40}{100}\frac{\text{ \%}}{\text{ \%}}\text{ = }\frac{x}{1200}\text{ }\frac{shares}{shares} \\ 100\cdot x=40\cdot1200 \\ x\text{ = }\frac{48000}{100}=480\text{ shares} \end{gathered}[/tex]Jill is packing a lunch to bring to school. There are 3 types of sandwiches to choose from and 4 types of fruit. For the drink, Jill has 2 options. How many different lunches can Jill pack?
To solve this problem, it is necessary to use the multiplication counting rule. It states that the total outcomes of two events a and b is the product of a and b, it means a*b.
In this case, the total outcomes is the product of the number of options for each event (sandwiches, fruits and drinks). This is 3*4*2.
[tex]3\cdot4\cdot2=24[/tex]There are 24 different lunches Jill can pack.
Tom is 26 years older than Paul. the product of his ages is 560. How old is Paul?
Given data:
The given age of Tom is T=P+26.
The expression for the product of their ages is TxP=560.
Substitute (P+26) for T in the second expression.
[tex]\begin{gathered} (P+26)P=560 \\ P^2+26P-560=0 \\ P^2+40P-14P-560=0 \\ P(P+40)-14(P+40)=0 \\ (P+40)(P-14)=0 \\ P=-40,\text{ 14} \\ P=14 \end{gathered}[/tex]Thus, the age of Paul is 14 years.
what digit is in the
Given x = 7, we have:
[tex]6x=6(7)=42[/tex]Answer: 42
Match the number with the corresponding letters(graphs). Note the number should have multiple graphs. Please answer 9
A function is increasing when the y-value increases as the x-value increases. A function is decreasing when the y-value decreases as the x-value increases.
The domain is the set of allowable x-values.
The following graphs as labelled changes from decreasing to increasing at least once:
C, K, O, M, R
Donovan wants to earn a 70% in Mr. Mottola's class. He knowshe currently has an 68% in the class after 7 grades. What is theminimum grade Donovan would need to earn in order to have a70%.
Let's check the information given so far to answer the question correctly:
Donovan target = 70%
Donovan currently average with 7 grades = 68%
Dr. Jordan is a veterinarian. The table shows the weights of 5 kittens at her office. What is the mean weight of the kittens? Kitten Weight (ounces) Kitten 1 6 Kitten 2 11 Kitten 3 6 Kitten 4 10 Kitten5 7
Recall that the mean of a given set of values is given as
[tex]\begin{gathered} \text{Mean = }\frac{sum\text{ of all the items or values}}{total\text{ number of item or values}} \\ =\text{ }\frac{6+11+6+10+7}{5} \\ =\frac{40}{5} \\ =8 \end{gathered}[/tex]x + 7y = -3 and y = 7x + 25. Are these parallel, perpendicular, or neither.
In order to know if those lines are parallel, perpendicular or neither we need to compare the slopes.
When two lines are parallel they have the same slope, when they are perpendicular their slopes are negative reciprocal, which means:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{Then} \\ m_1\cdot m_2=-1 \end{gathered}[/tex]Now, we need to arrange both equations into the slope-intercept form y=mx+b
Where m is the slope and b is the y-intercept.
The second line is already in slope-intercept form:
[tex]y=7x+25[/tex]Thus, its slope is 7.
The first line in slope-intercept form is:
[tex]\begin{gathered} x+7y=-3 \\ 7y=-3-x \\ y=\frac{-3-x}{7} \\ y=\frac{-3}{7}-\frac{x}{7} \\ \text{ By reordering terms} \\ y=-\frac{x}{7}-\frac{3}{7} \end{gathered}[/tex]Then it slope is -1/7.
Their slopes are not the same, then they aren't parallel, but let's check if they are perpendicular:
[tex]\begin{gathered} m1\cdot m2=-1 \\ -\frac{1}{7}\cdot7=-1 \\ -1=-1 \end{gathered}[/tex]They are negative reciprocal, then they are perpendicular lines.
5x + 9y = 31 and - 2x - y = 11
5x + 9y = 31 -------------(1)
-2x - y = 11 ---------------(2)
Multiply through equation (2) by 9
-18x - 9y = -99---------------(3)
Add equation(1) and (2)
-13x = -68
Divide both-side by -13
x = 5.23
Substitute x in equation(1) and solve for y
-2(5.23) - y = 11
-10.46 - y = 11
Solve 2(x+7)-34=4x-11x+4(x-1)
Given:
There are given the equation:
[tex]2(x+7)-34=4x-11x+4(x-1)[/tex]Explanation:
To solve the above equation, we need to use the above equation:
[tex]\begin{gathered} 2(x+7)-34=4x-11x+4(x-1) \\ 2(x+7)-34=4x-11x+4x-4 \\ 2(x+7)-34=-3x-4 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2(x+7)-34=-3x-4 \\ 2(x+7)-34+3x+4=0 \\ 2x+14-34+3x+4=0 \\ 2x+18-34+3x=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2x+18-34+3x=0 \\ 5x-16=0 \\ 5x=16 \\ x=\frac{16}{5} \end{gathered}[/tex]Final answer:
Hence, the value of x is shown below:
[tex]x=\frac{16}{5}[/tex]An initial amount of money is placed in an account at an interest rate of 1% per year, compounded continuously. After six years, there is $1083.07 in the account. Find the initial amount placed in the account. Round your answer to the nearest cent.
We have to find the initial value in the account.
The interest rate is r = 1% = 0.01.
The time period is t = 6.
The final value after 6 years is FV = 1083.07.
The interest is compounded continously.
We can relate the present value PV with the other variables as:
[tex]\begin{gathered} FV=PVe^{rt} \\ PV=FVe^{-rt} \\ PV=1083.07\cdot e^{-0.01\cdot6} \\ PV=1083.07\cdot e^{-0.06} \\ PV\approx1083.07\cdot0.94176 \\ PV\approx1020.00 \end{gathered}[/tex]Answer: the initial amount was $1020.00
Hi! I need help with a couple math questions but heres this oneTriangle XYZ is located at X (−2, 1), Y (−4, −3), and Z (0, −2). The triangle is then transformed using the rule (x−1, y+3) to form the image X'Y'Z'. What are the new coordinates of X', Y', and Z'?
Transformation rule:
[tex](x,y)\rightarrow(x-1,y+3)[/tex]Given triangle XYZ
To get X'Y'Z' coordinates of vertices, subtract 1 to the x coordinate and add 3 to the y-coordinate:
[tex]\begin{gathered} X(-2,1)\rightarrow X^{\prime}(-2-1,1+3) \\ X^{\prime}(-3,4) \end{gathered}[/tex][tex]\begin{gathered} Y(-4,-3)\rightarrow Y^{\prime}(-4-1,-3+3) \\ Y^{\prime}(-5,0) \end{gathered}[/tex][tex]\begin{gathered} Z(0,-2)\rightarrow Z^{\prime}(0-1,-2+3) \\ Z^{\prime}(-1,1) \end{gathered}[/tex]Then, the coordinates of vertices in triangle X'Y'Z' are: X'(-3,4), Y'(-5,0) and Z'(-1,1)Find an equation for the line below.A(5,1) B(-4,5)
The equation of a line has always the form
[tex]y=m\cdot x+b[/tex]where "m" is called its slope, and "b" is called its y-intercept. It's a well-known fact that m can be calculated using two points of the line. Let's use A and B:
[tex]m=\frac{-5-1}{-4-(5)}=\frac{-6}{-9}=\frac{6}{9}=\frac{2}{3}[/tex]Then, our equation becomes
[tex]y=\frac{2}{3}x+b[/tex]Replacing A there, we get
[tex]\begin{gathered} 1=\frac{2}{3}(5)+b\Rightarrow1=\frac{10}{3}+b\Rightarrow\ldots \\ \ldots b=1-\frac{10}{3}=-\frac{7}{3} \end{gathered}[/tex]Having found m and b, the final answer is
[tex]y=\frac{2}{3}x-\frac{7}{3}[/tex]Prescription 1: According to the eScience Lab Manual for Lab 1, Experiment 3, you need to prepare 65 mL of a 60% soda/syrup “prescription”.To do this, you can use the 80% soda solution and the syrup solution (0% strength) that you have in inventory.How many mLs of soda solution do you need to create this final solution?
Let:
x = mL of soda solution
y = mL of syrup solution
The soda solution is 80% strength and the syrup solution is 0% strength, thus the combination of x and y of each solution gives strength of:
80x + 0y
This combination must be 60% strength, thus:
80x + 0y = 60(x + y) [1]
The total amount of solution is 65 mL, thus:
x + y = 65
Substituting in [1]
80x + 0y = 60*65
Operating and simpliifying:
80x = 3900
Dividing by 80:
x = 48.75
I need 48.75 mL of soda solution
hi, I actually have this question not this one sorry
we know that
If V is the midpoint of SU
then
SV=VU
substitute the given values
2x+18=8x-6
solve for x
8x-2x=18+6
6x=24
x=4Find SV
SV=2x+18
SV=2(4)+18
SV=26 unitsso
VU=26 unitsand
SU=2SV
SU=2(26)
SU=52 unitsSolve this system of equations by graphing. First graph the equations, and then type the solution.y=x+7y= –7/3x-3
Solution
For this case we have the following system of equations:
y= x+7
y= -7/3 x -3
We can create the plot and we got:
Then the answer for this case should be:
x= -3 and y= 4
Tanner wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3/4 m by 3 1/2 m. Find the area the grass seed needs to cover
The area of the pool that Tanner does not need to cover is
20.125 square meters
Dimensions of the pool:
Length = 5 3/4 m by 3 1/2 m
area of rectangular pool
= product of dimensions
= 23/4 × 7/2
=20.125 square meters
Area is a unit of measurement used to describe a region's size on a flat or curved surface. While the area of a plane region or plan area refers to the area of a shape or planar lamina, surface area refers to the volume of a raised platform or the edge of a three-dimensional object.
Area is the two-dimensional equivalent of the volume of a solid as well as the length of a curve (a one-dimensional term). It can be compared to the amount of material of a certain thickness needed to create a model of the shape or the amount of paint needed to completely cover a surface in one application.
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Graph the set {x | x≥-1) on the number line.Then, write the set using interval notation.
Answer:
Interval Notation: (-1, ∞)
Explanation:
Given the set:
[tex]\{x|x\ge-1\}[/tex]The graph of the set on the number line is attached below.
Note that all values of x greater than -1 are to the right of -1.
Next, the set written using the interval notation is:
[tex](-1,oo)[/tex]