ANSWER
[tex]y-1= \frac{1}{3} (x- 6)[/tex]
EXPLANATION
We want to write the point-slope form of the line that passes through (6, 1) and is perpendicular to a line with a slope of -3.
The slope of this line is negative reciprocal of -3.
[tex]m = - \frac{1}{ - 3} = \frac{1}{3} [/tex]
The point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and the slope to get;
[tex]y-1= \frac{1}{3} (x- 6)[/tex]
Answer:
y - 1 = 1/3*(x - 6)
Step-by-step explanation:
point-slope form of a line:
y - y1 = m*(x - x1)
where x1 and y1 are the coordinates of the point included in the line and m is its slope.
Two lines are perpendicular when the multiplication of their slopes is equal to -1. In this case,
m*(-3) = -1
m = 1/3
Replacing this slope and the coordinates of point (6, 1) we get:
y - 1 = 1/3*(x - 6)
If you have two dice and you roll one, what is the probability the second dice is less than or equal to the first dice number?
Answer:the probability is 0.5
Step-by-step explanation:
Fine the solution set 6x^2+x-1=0 separate the two values with a comma
Answer:
see explanation
Step-by-step explanation:
Given
6x² + x - 1 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 6 × - 1 = - 6 and sum = + 1
The factors are + 3 and - 2
Use these factors to split the x- term
6x² + 3x - 2x - 1 = 0 ( factor the first/second and third/fourth terms )
3x(2x + 1) - 1(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(3x - 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = [tex]\frac{1}{3}[/tex]
The area of a rhombus is 65 square units. The length of one diagonal is 13 units. What is the length of the other diagonal? 5 units 6 units 10 units 12 units
Answer:
The length of the other diagonal is 10 units
Step-by-step explanation:
we know that
The area of a Rhombus is equal to
[tex]A=\frac{1}{2}[D1D2][/tex]
where
D1 and D2 are the diagonals of the rhombus
we have
[tex]A=65\ units^{2}[/tex]
[tex]D1=13\ units[/tex]
substitute in the formula and solve for D2
[tex]65=\frac{1}{2}[(13)D2][/tex]
[tex]130=[(13)D2][/tex]
[tex]D2=130/13=10\ units[/tex]
Answer:
10
Step-by-step explanation:
Consider the following figure. Which of the following statements are true? Select all that apply. (Answer choices are in the picture)
Answer:
D and E
Step-by-step explanation:
2 and 3 are verticle angles
1 and 4 add up to more than 180
angles 1 2 and 3 add up to more than 180
Based on the figure, the statements are true include;
D. m∠3 ≅ m∠4 = m∠1 ≅ m∠2
E. m∠1 ≅ m∠4 are vertical angles.
What is the vertical angles theorem?In Mathematics and Euclidean Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two lines intersect each other are always congruent, which means being equal to each other.
By applying the vertical angles theorem to the lines, we have the following congruent angles:
m∠1 ≅ m∠4
m∠2 ≅ m∠3
Based on linear pair theorem, we have the following supplementary angles;
m∠3 + m∠4 = 180°
m∠1 + m∠2 = 180°
m∠3 ≅ m∠4 = m∠1 ≅ m∠2 (transitive property).
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A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if: Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 8 cm, BC = 6 cm. Find r.
Answer:
The radius of circle is 5 cm
Step-by-step explanation:
Given a right triangle △ABC with right angle C is inscribed in a circle in which
m∠C = 90°, AC = 8 cm, BC = 6 cm
we have to find the radius of circle.
As ACB is right angles triangle where angle C is right angle.
⇒ side AB must be the diameter of circle as angle made at semi circle is 90°
[tex]Radius=AO=\frac{1}{2}AB[/tex]
By Pythagoras theorem
[tex]AB^2=AC^2+CB^2[/tex]
[tex]AB^2=8^2+6^2=64+36=100[/tex]
[tex]AB=10cm[/tex]
[tex]Radius=AO=\frac{1}{2}AB=\frac{1}{2}\times 10=5cm[/tex]
Hence, the radius of circle is 5 cm
The rectangular prism has a volume of 93 cubic centimeters. Which equation can be used to find the height, h, of the prism? A.h = 93 × 15 . 5 B.ℎ=93.5×15.5×15.5 C.ℎ=93/15.5 D.h = 15 . 5/93
Answer: option C
Step-by-step explanation:
The volume of a rectangular prism can be calculated with this formula:
[tex]V=l*w*h[/tex]
Where "V" is the volume of the prism "l" is the lenght, "w" is the width and "h" is the height.
You know that the volume of this prism is 93 cubic centimeters and you need to find the height. Then, you have to solve for "h":
[tex]h=\frac{V}{l*w}[/tex]
You can observe that the volume is in the numerator and the product of the lenght and the width of the rectangular prism is in the denominator, then, the option that matches this form is the option C:
[tex]h=\frac{93}{15.5}[/tex]
Answer:
H= 93/15.5
Step-by-step explanation:
ABC bank requires a 20% down payment on all of its home loans if a house is priced at 185000 what is the amount of the down payment required by the bank?
It would be 37’000 because 20% of 185000 is 37’000 which you get by 20 x 185000 and dividing the answer to 100.
pleas solve this equation
2x+9+3x+x=
6x + 9
Combine the like terms. 2x + 3x + x = 6x, and 9 just stays the same. This is as simple as the equation can get without knowing what 2x + 9 + 3x + x equals.
If 2x+9+3x+x= then 6x+9 will be x= 15
3x = 2* + 25
IF YOU HELP YOU GET BRAINLIEST PLEASE HELP FAST
Is the answer 25? Thats what I got.
If the sum of five odd consecutive integers is 295. What is the middle integer?
Answer:
59Step-by-step explanation:
n - 4, n - 2, n, n + 2, n + 4 - five odd consecutive integers
The equation:
(n - 4) + (n - 2) + n + (n + 2) + (n + 4) = 295 combine like terms
(n + n + n + n + n) + (-4 - 2 + 2 + 4) = 295
5n = 295 divide both sides by 5
n = 59
Mustafa buys seed packets for a community garden. One packet of basil seeds costs $1.50. One packet of squash seeds costs $2.50. Let b represent the number of packets of basil seed. Let s represent the number of packets of squash seeds. Mustafa spent $38 on 18 packets of seeds. How many packets of each type of seeds did Mustafa buy?
Answer:
Step-by-step explanation:
b+s=18
s=18-b
1.50 b+2.50 s=38
multiply by 4
6.00 b+10.00 s=152
divide by 2
3 b+5 s=76
3 b+5(18-b)=76
3 b+90-5 b=76
-2b=76-90
-2b=-14
divide by -2
b=7
s=18-7=11
There are total 11 packets of squash seeds and 7 packets of basil seeds.
What is system of linear equations?A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
What is substitution method?The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.
According to the given question.
Cost of one packet of basil seeds = $1.50
Cost of one packet of squash seeds = $2.50
Cost of 18 packets of seeds = 38
Also, b represents the number of packets of basil seeds and s represents of numbers of squash seeds.
Therefore, from the given conditions we get some system of equations
[tex]s + b = 18..(i)[/tex]
and [tex]b(1.50) + s(2.50) = 38...(ii)[/tex]
From equation (i)
[tex]s = 18-b[/tex]
Substitute the value of s in the equation (ii)
⇒[tex]1.50b+(18-b)2.50 =38[/tex]
⇒ [tex]1.50b + 45 - 2.50b = 38[/tex]
⇒[tex]-b = 38-45[/tex]
⇒ [tex]-1b =- 7[/tex]
⇒[tex]b = 7[/tex]
So, [tex]s = 18 - 7 =11[/tex]
Hence, there are total 11 packets of squash seeds and 7 packets of basil seeds.
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Archie rolls two number cubes, each with sides numbered 1 through 6. He then finds the sum of the numbers on the top of the cubes.
Which two sums have the the same probability?
Your probability of getting a specific number on a die is 1/6. Since you have 2 dice the probability for each is 1/6. Multiply those together to find the probability that the numbers would be the same. So, 1/36 is the correct answer.
(3a ^3)^x = 27a^9
what’s the value of x?
Answer:
x = 3Step-by-step explanation:
[tex](3a^3)^x=27a^9\\\\(3a^3)^x=3^3a^{3\cdot3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(3a^3)^x=3^3(a^3)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\(3a^3)^x=(3a^3)^3\iff x=3[/tex]
What is the solution to his equation 2x+6=20
2x+6=20
move 7 to the right side.
The sign changes from positive to negative. whenever moving a number to the other side the sign changes.
2x+6-6=20-6
2x= 14
Divide by 2 for both of the numbers
x=7
check answer:
Substitute x into the equation
2(7)+6=20
20= 20
Answer: x=7
The solution of the given linear equation in one variable is x = 7.
What are linear equations?The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2.
Given is a linear equation in one variable, 2x+6 = 20,
We need to find its solution,
Since, the given linear equation has only one variable, so it will have only one solution.
The equation is =
2x+6 = 20
Solving for x,
2x = 20-6
2x = 14
x = 7
Hence, the solution of the given linear equation in one variable is x = 7.
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Please solve and give answer
ANSWER
domain:
[tex]x \geqslant - 3[/tex]
Range
[tex]y \leqslant - 2[/tex]
EXPLANATION
The given function is
[tex]f( x) = - \sqrt{x + 3} - 2[/tex]
This base of this function is
[tex]y = \sqrt{x} [/tex]
This function has been shifted to the left 3 units and down 2 units.
This function is reflected in the x-axis.
Therefore graph starts at (-3,-2) and move down forever.
The domain is obtained using the expression under the radical sign.
It must be greater than or equal to zero.
[tex]x + 3 \geqslant 0[/tex]
[tex]x \geqslant - 3[/tex]
The range is
[tex]y \leqslant - 2[/tex]
Iterations question two need help please :)
Answer:
option b
1 , 16, 121 , 13456
Step-by-step explanation:
Given in the question a function, f(x) = (x - 5)²
initial value [tex]x_{0}[/tex] = 4
First iteration
f(x0) = f(4) = (4 - 5)² = (-1)² = 1
x1 = 1
Second iteration
f(x1) = f(1) = (1 - 5)² = (-4)² = 16
x2 = 16
Third iteration
f(x2) = f(16) = ( 16 - 5)² = (11)² = 121
x3 = 121
Fourth iteration
f(x3) = f(121) = (121 - 5)² = (116)² = 13456
x4 = 13456
What is the measure of angle ABC?
Answer:
42.5
Step-by-step explanation:
110 - 25 divided by 2 because
angle ABC = (angle AC- angle DE)÷2
simplify
[tex] \frac{x^{2} + 12x + 36 }{x^{2} + 4x - 12 } [/tex]
Answer:
(x-2)/(2x+8)
Step-by-step explanation:
The first step to solve this expression is to use a² - 2a b + b² = (a - b)² to factor the expression
Factor out 2 from the expression
Write 2x as a difference
Factor out x from the expression
Factor out -2 from the expression
Factor out x + 4 from the expression
Reduce the fraction with x - 2
Finally,, distribute 2 through the parenthesis to find your answer
This means that the correct answer to your question is (x-2)/(2x+8)
Answer:
x + 6
----------- for all x EXCEPT x = -6
x + 2
Step-by-step explanation:
Note that the numerator, x^2 + 12 x + 36, factors into (x + 6)^2, and that
the denominator factors into (x + 6)(x - 2).
Thus, the given expression reduces to:
(x + 6)(x + 6)
-----------------------
(x + 6)(x + 2)
and can be reduced to:
x + 6
----------- This is true for all x EXCEPT x = -6. At x = -6, the expression
x + 2 is not defined.
Whch experision is equialent to 5(4x+3)-2x?
A.18x+15
B.18x+3
C.7x+8
D.2x+8
Answer:
The correct answer is option A. 18x + 15
Step-by-step explanation:
It is given an expression in variable x,
5(4x + 3) - 2x
To simplify the given expression
5(4x + 3) - 2x = (5 * 4x) + (5 * 3) - 2x (open the bracket)
= 20x + 15 - 2x
= 20x - 2x + 15
= 18x + 15
Therefore the correct answer is 18x + 15
The correct option is option A. 18x + 15
Which equation could be used to find the number of scarves, x, Syrilla needs to sell in order to earn $200? I don’t know the work
Answer:
Step-by-step explanation:
(1) 4x = 200
(2) 50
Answer:
4x = 200
50
Step-by-step explanation:
One scarf = $4
Number of scarves = x
Amount she needs to earn = $200
Equation
4x = 200
Number of scarves
= 200 ÷ 4
= 50
Write a function for the situation described and find the value after 7 yrs. A $16,800 car depreciates 11% each year
Answer:The starting value is 20,300, and the value is decreasing by 9.5% each year.
Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.
A decrease by 9.5% corresponds to multiplying by 91.5% each year.
We write . We plug in 11 years for t.
$7,671.18
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Step-by-step explanation:
Answer:
The starting value is 20,300, and the value is decreasing by 9.5% each year.
Step-by-step explanation:
Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.A decrease by 9.5% corresponds to multiplying by 91.5% each year.We write . We plug in 11 years for t.
The equation of a circle is x^2+y^2+18x+4y+49=0. What are the center and the radius of the circle?
please help I am failing math and have no idea what's :) going :) on :) in :) class :)
Answer:
Center: (-9, -2)
Radius = 6
Step-by-step explanation:
The general equation of the circle is:
[tex]x^{2} + y^{2}+2gx+2fy+c=0[/tex]
The center of the circle is given as (-g, -f) and the radius of this circle is calculated as:
[tex]r=\sqrt{g^{2}+f^{2}-c}[/tex]
The given equation is:
[tex]x^{2} +y^{2}+18x+4y+49=0[/tex]
Re-writing this equation in a form similar to general form:
[tex]x^{2} +y^{2}+2(9)(x)+2(2)(y)+49=0[/tex]
Comparing this equation with general equation we get:
g = 9
f = 2
c = 49
Thus center of the given circle is (-g, -f) = (-9, -2)
The radius of the circle will be:
[tex]r=\sqrt{9^{2}+2^{2}-49}=6[/tex]
Thus the radius of the given circle is 6.
Help! Ill mark you as brain! 15 points!
Answer:
35 in²
Step-by-step explanation:
The irregular shaped can be divided into two squares and one rectangle, so the area will be the additions of the area of the squares and the rectangle
area of square A = L *B = 3 *3 = 9in²
area of square B = L * B = 4*4 = 16in²
area of rectangle C = L * B = 5 *2 = 10in²
th area of the irregular shape = 9 in² + 16 in² + 10 in² = 35 in²
A jet travels 600 miles in 5 hours. At this rate, how far could the jet fly in 14 hours. What is the rate of speed of the jet?
Find the jets speed per hour by dividing distance by time:
600 miles / 5 hours = 120 miles per hour. ( Rate of speed)
Now multiply the speed by time:
120 miles per hour x 14 hours = 1,680 miles.
Answer:
120 miles per hour
Step-by-step explanation:
Jonna needs to travel 496 miles in 8 hours. How fast does she need to go in order to reach her destination on time?
Answer:62
Step-by-step explanation:
Which of these tables represents a non-linear function?
Answer:
The third table
Step-by-step explanation:
A linear function must increase or decrease at a constant rate. All the tables either add 1 or subtract 1 each time x increases except for the third one which at one point adds two. This is not a consistent increase and therefore is not linear
Answer:
3ed tabel
Step-by-step explanation:
adds 1 to both sides so its a non leirn
25 POINTS!!
The diagram below shows the percentages of people attending a football game who were supporters of either the home team or the visiting team.
the home team: 80%
visiting team: 20%
if the total number of people attending the game
was 64,000, how many people were supporters of the home team?
A, 12,800
B, 38,4000
C, 48,000
D, 51,200
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Answer:
The answer is D. 51,200
Step-by-step explanation:
64000/x=100/80
(64000/x)*x=(100/80)*x - we multiply both sides of the equation by x
64000=1.25*x - we divide both sides of the equation by (1.25) to get x
64000/1.25=x
51200=x
x=51200
The number of people who were supporters of the home team is 51,200, the correct answer is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The home team= 80%
Visiting team= 20%
Now,
If 80% of the people attending the football game were supporters of the home team, then we can find the number of people who were supporters of the home team by multiplying the total number of people attending the game by 80%:
= 0.8 * 64,000
= 51,200
Therefore, by algebra the answer will be 51,200.
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Legit about to be done with pathway please help, OFFERING 20 points k? please tho
Answer:
The answer in the attached figure
Step-by-step explanation:
step 1
Find the area of one blue square
[tex]A=6^{2}=36\ ft^{2}[/tex]
step 2
Find the area of one orange triangle
[tex]A=(1/2)8^{2}=32\ ft^{2}[/tex]
Part 1) [tex]256\ ft^{2}[/tex]
Divide the total area by the area of one orange triangle
[tex]256/32=8\ triangles[/tex]
Part 2) [tex]180\ ft^{2}[/tex]
Divide the total area by the area of one blue square
[tex]180/36=5\squares[/tex]
Part 3) [tex]168\ ft^{2}[/tex]
Let
x----> the number of blue squares
y ------> the number of orange triangles
we know that
[tex]36x+32y=168[/tex]
Construct a table and prove different values for x and for y
we have
x=2, y=3
Two blue squares and three orange triangles
Area of blue squares
[tex]A1=2*(36)=72\ ft^{2}[/tex]
Area of an orange triangles
[tex]A2=3*(32)=96\ ft^{2}[/tex]
so
the area total is
[tex]72+96=168\ ft^{2}[/tex]
hugo must divide 5 apples among his 3 nephews. Each nephew receives the same amount, and there are no apples left over. How many apples did each nephew receive?
Answer:
D
Step-by-step explanation:
5 divided by 3 is 1.6666 which is the same as 1 and 2/3
The correct answer is D
f(x)=2x an$ g(x)=2x+3,what is the value of f(g(-8))
First plug in g(x) into f(x)
F((g(x))=2(2x+3)
And now you plug in -8
F(g(-8))=2(-16+3)
F(g(-8))=2(-13)
F(g(-8))=-26