Answer:
[tex]y = - \frac{1}{3} x - 4[/tex]
Step-by-step explanation:
The equation of a kind can be written in the slope intercept form, y= mx +c, where m is the gradient and c is the y-intercept.
[tex]\boxed{gradient = \frac{y1 - y2}{x1- x2} }[/tex]
[tex]m = \frac{ - 2 - ( - 3)}{ - 6 - ( - 3)} [/tex]
[tex]m = \frac{ - 2 + 3}{ - 6 + 3}[/tex]
[tex]m = \frac{ 1}{ - 3} [/tex]
Substitute the value of m into the equation:
[tex]y = - \frac{1}{3} x + c[/tex]
To find the value of c, substitute a pair of coordinates.
When x= -3, y= -3,
[tex] - 3 = - \frac{1}{3} ( - 3) + c[/tex]
[tex] - 3 = 1 + c[/tex]
c= -3 -1
c= -4
∴ The equation of the line is [tex]y = - \frac{1}{3} x -4[/tex].
The length of a rectangle is four times its width. If the area of the rectangle is 196 yd², finds its perimeter.
Answer:
perimeter = 70 yards
Step-by-step explanation:
⭐What is the area of a rectangle?
area = length * width⭐What is the perimeter of a rectangle?
perimeter = 2(length) + 2(width)Strategy1. Make the equation for the area of the given rectangle and solve for x
2. Substitute x into the expressions of the length and width and solve for the perimeter
Working1. Define the expressions of the length and width of the rectangle
width: x
length: 4x
2. Make the equation for the area of the rectangle
[tex]196yd^2 = 4x * x\\196yd^2 = 4x^2[/tex]
3. Solve for x
[tex]\frac{196}{4} = x^2[/tex] . . . . . . . . . . divide both sides by 4
[tex]49 = x^2[/tex]
[tex]\sqrt{49} = \sqrt{x^2}[/tex] . . . . . . . . square root both sides to isolate x
∴ [tex]7 = x[/tex]
4. Substitute x into the expressions of the length and the width
width: x
width = 7
height: 4x
height = 4(7) = 28
5. Solve for the perimeter
[tex]perimeter = 2(length) + 2(width)[/tex]
[tex]perimeter = 2(28) + 2(7)\\perimeter = 56 + 14\\perimeter = 70[/tex]
IF THIS RESPONSE HELPED YOU, PLEASE MARK IT THE "BRAINLIEST"! :)
Can someone help me figure this out?
Answer:
x^3
Step-by-step explanation:
In 2-4, write yes or no to indicate whether the expressions are equivalent. Grade 6 math, please help
Don has 6 pieces of pipe. Each piece is 2 feet 6 inches long.
If Don joins the pieces end to end to make one long pipe, how long will the new pipe be?
The pipe will be
feet
inches long.
Answer: 15 feet
Step-by-step explanation:
First you start with 2ft and 6in and convert it all into into inches.
If you know that 1 ft=12in then you know that 2 feet is the same as saying
12+12=24. If you don't understand use this chart-
1 ft=12in
2ft= 24in
3ft= 36in
4ft =48in
5ft= 60in
6ft= 72in
see I am counting by 12's.
Now take 2ft and convert it into inches. That would be 24 in (look in the chart).
now take the 24in(2ft) and add it to the 6in. So 24+6 =30
So now you know that one piece of pipe is 30in long.
But in the text it states that Don has 6 pieces, so...
because it says that he has 6 pieces of pipe then you are going to take that and multiply that number(6) by how long each piece is. look up and it shows how long each pieces is. They are all each 30in long. Take 30 and multiply that by 6 because there are 6 pipes and you will get 120in.
But it says that they need an answer of feet and inches or just feet if it exactly a some sort of foot like 43feet or 2 feet.
So then we are going to convert 180 into feet by dividing 180 by 12 and you get 15. So the answer is 15.
I hope this helps. Have fun learning!!
Answer:
The pipe will be 15 feet 0 inches long.
Step-by-step explanation:
1 pipe is 2 feet 6 inches long
There are 6 pieces
6×2= 12 feet 6×6= 36 inches
The pipe will be 12 feet 36 inches long, however, there are 12 inches in a foot so we can covert the inches to feet
36 inches ÷ 12 inches = 3 feet
12 feet + 3 feet = 15 feet
The pipe will be 15 feet 0 inches long.
There are 9 players on a baseball team there are 6 teams in the league how many baseball players are in the league
Answer:
54
Step-by-step explanation:
Multiply 9 (players per team) and 6 (teams in the league) to find the total players in the league.
9 times 6 = 54
who is the richest president in the world
The richest president in the world is Sebastian Pinera, President of Chile with $2.4 billion.
please answer in full process
questions
Given L || M find the value of unknown angles in each of the following figures
Answer:
Angle x = 120 degrees
Angle y = 60 degrees
Step-by-step explanation: Angle x has to be equivalent to the 120 degree angle that is already given since lines l and m are parallel as well as lines p and q. To find angle y, you must realize that angles x and y are supplementary angles, so their sum is 180 degrees. Since we now know that angle x is 120 degrees, you must subtract 120 from 180 in order to find the value of angle y: 180 - 120 = 60 degrees. I'm sure that there are other methods to figuring this question out, but this is how I did it.
Geometry need help asap
On solving the provided question, we can say that - here in quadrilateral we have x + 146 + 47 + y = 360 => [tex]x= 83.5[/tex]
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here,
x + 146 + 47 + y = 360
2x + 193 = 360
2x = 167
[tex]x= 83.5[/tex]
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Please help giving brainliest
Answer:
look at the picture I sent
Now you will write an informative paragraph that will help Frankie to understand his financial options and formulate best practices for spending and saving.
Answer:
Strategies that Frankie should consider:
1.) What he needs vs what he wants (does Frankie need new shoes?)
2.) Opportunity cost (savings Frankie would have to give up if he buys new shoes)
3.) Short-term and long-term goals (Does Frankie needs shoes now, or can he wait?)
Frankie should think about a number of options before purchasing a new pair of shoes. He should first consider whether he actually needs or wants these shoes. He should then think about opportunity cost. How else could he have used that money if he had not purchased the shoes? Could he have utilized his resources more effectively? He must also think about the issue of setting goals. He needs to decide if this is a task for the present or the future.
Also I dont understand how this is math
Convert without rounding 1/8 to a decimal
Answer:
0.125
Step-by-step explanation:
Step 1: Find a number such that we can multiply by the denominator of the fraction to make it 10 or 100 or 1000 and so on
Step 2: Multiply both numerator and denominator by that number to convert it into it's equivalent fraction.
Step 3. Then write down just the numerator, putting the decimal point in the correct place i.e., one space from the right hand side for every zero in the denominator
1/8 = (1×125)/(8×125) = 125/1000 = 0.125
Thus, as a decimal 1/8 is 0.125
please help will give brainliest if correct
Answer:
A
Step-by-step explanation:
Find the product
(2z+9)(z-7)
Answer:
2z^2-5z-63
Step-by-step explanation:
2z^2+9z-14z-63
2z^2-5z-63
please answer the following question, AND NO LINKS OR YOU WILL GET REPORTED.
Answer:
Mode
Step-by-step explanation:
I believe mode because 8 is the number that appears most often in this set of numbers.
note: Mode is the number that appears most often in any set of numbers.
Which equation has a solution of for n? 3 re
Answer:
you dont have a picture
Step-by-step explanation:
Find the length of side xx in simplest radical form with a rational denominator. 3
The length of x is 6 in simplest radical form.
What is a right-angled triangle?'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'
According to the given ,
Perpendicular = 3
Hypotenuse = x
We know,
sin∅ = 3/x
∅ = 30°
⇒ sin30 = 3/x
⇒ 1/2 = 3/x [ sin30 = /2 ]
⇒ x = 3 * 2
⇒ x= 6
Hypotenuse = 6
Applying Pythagoras theorem:
Hypotenuse² = Perpendicular² + Base²
6² = 3² + Base²
6² - 3² = Base²
Base² = 25
Base = √25
Base = 5
We can conclude the value of x to be 6.
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Rewrite without parentheses and simplify.
(V+2)^2
Answer:
V^2 + 4V + 4
Step-by-step explanation:
the area of a circle is 154cm, calculate it's radius?
Answer:
r = 7
Step-by-step explanation:
area equals (pi)(r)^2
first divide 154 by pi
154/pi = 49
r^2 = 49
square root both sides
r = 7
5 Find 6 in Surface Area
Answer:
8 x 6 = 48
48 divided by 2 = 24
24 x 2 = 48
10 x 12 = 120
120 x 2 = 240
8 x 12 = 96
Add all given areas:
48 + 96 + 240 = 384 in2 is your answer.
Five increased by the product of a number and 9 is greater than -27
As an inequality
Answer:
brhnrnr e euebe ehe we je euebe ejeje
Please help, consider function f. F(x) = square root x-1 which graph represents function f?
Answer:
still waiting for the ai to solve it
A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the function f(x)=√(x-1), therefore, the function can be represented on the graph as is Y.
Hence, the correct option is C.
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Let L be the line through A = (1, 2,−1) and B = (5,−3, 4).
Answer the following questions below:
1. Find a direction vector of L
2. Find a parameterization of L.
3. Find the two points on L that are at distance 2 away from A.
4. Find a unit speed parameterization of L.
Answer:
(4, -5, 5)L = (1+4t, 2-5t, -1+5t)(1+4√66/33, 2-5√66/33, -1+5√66/33), (1-4√66/33, 2+5√66/33, -1-5√66/33)(1-2t√66/33, 2+5√66/66, -1-5√66/66)Step-by-step explanation:
Given L is the line through A(1, 2, -1) and B(5, -3, 4), you want its direction vector, a parameterization of L, 2 points on L that are 2 units from A, and a unit speed parametrization of L.
1. Direction vectorA direction vector for L will be the vector AB.
[tex]\overrightarrow{AB}=B-A=(5,-3,4)-(1,2,-1)\\\\\boxed{\overrightarrow{AB}=(4, -5,5)}[/tex]
2. Parameterized lineThe parameterized equation will be ...
[tex]L=A+t\cdot\overrightarrow{AB}\\\\\boxed{L=(1+4t,2-5t,-1+5t)}[/tex]
3. Distance 2The direction vector has length √66, so we can find two points on L that are 2 units from A by using t = ±2/√66 in the parameterized equation.
Here, they are:
P1 = L(2/√66) = (1 +8/√66, 2 -10/√66, -1 +10/√66)
P2 = L(-2/√66) = (1 -8/√66, 2 +10/√66, -1 -10/√66)
In the Answer section above, these are written with rationalized denominators.
4. Unit speedThe unit speed parametrization uses the unit direction vector instead of the unnormalized direction vector in the parameterized equation. Effectively, t is scaled by a factor of 1/√66.
L = (1 +4t/√66, 2 -5t/√66, -1 +5t/√66)
In the Answer section above, this is written with rationalized denominators.
You might notice here that it is easier to answer part 3 if you have this equation. You need only substitute t=±2 to get the points 2 units from A.
Help with both questions (8 and 9) please.
No link answers thx
Step-by-step explanation:
8.
Let the number is x. A number minus 7 is (x-7). It is doubled to get 86. So,
[tex](x-7)^2=86\\\\x-7=\sqrt{86}\\\\x-7=\pm 9.27\\\\x-7=9.27\ and\ x-7=-9.27\\\\x=16.27\ or\ x=-2.27[/tex]
The number can be 16.27 or -2.27.
9.
The diameter of the cylindrical tank, d = 20 ft
Radius, r = 10 ft
It is filled with oil to a depth of h feet.
The volume of a cylindrical shaped object is given by :
[tex]V=\pi r^2 h[/tex]
Put the given values,
[tex]V=\pi (10)^2h\\\\V=3.14\times 100\times h\\\\V=314h\ ft^3[/tex]
So, the volume of the tank is equal to [tex]314h\ ft^3[/tex].
Part 5: Identify key features and graph a hyperbola from general form.
Answer the following questions to determine the key features of the hyperbola based on the equation
shown, and then graph it.
4x^2 + 8x – 9y^2 – 36y – 68 = 0
a) Write the standard equation of the hyperbola. (3 points)
b) What is the center of the hyperbola? (1 point)
c) What are the foci of the hyperbola? (2 points)
d) What are the asymptotes of the hyperbola? (2 points)
e) Sketch a graph of the hyperbola and label the center, foci, guiding box, and asymptotes. (4 points)
a) [tex]\frac{(x+1)^{2}}{3^{2}}-\frac{(y+2)^{2}}{2^{2}} = 1[/tex].
b) (h, k) = (-1, -2).
c) F₁ (x, y) = (-1 - √13, -2), F₂ (x, y) = (-1 + √13, -2).
d) y = ±2 · (x + 1) / 3 - 2.
e) See the image attached below.
How to analyze a hiperbolaIn this question we must analyze the general equation of a hyperbola and derive all the required information by algebraic and graphic means. All this information is derived from the standard equation of the hyperbola, which is presented below:
[tex]\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}} = 1[/tex] (1)
Where:
a - Horizontal axis distanceb - Vertical axis distance h, k - Coordinates of the center of the hyperbola.The foci are located at the following two points: [tex]F_{1} (x, y) = (h - c, k)[/tex], [tex]F_{2} (x,y) = (h + c, k)[/tex].
Where [tex]c = \sqrt{a^{2}+b^{2}}[/tex].
And the asymptotes of the hyperbola are described by the following formulas:
y₁ = b · (x - h) / a + k (2)
y₂ = - b · (x - h) / a + k (3)
a) We transform the general equation into its standard form:
4 · x² + 8 · x - 9 · y² - 36 · y - 68 = 0 Given(2 · x)² + 4 · (2 · x) - (3 · y)² - 12 · (3 · y) - 68 = 0 Definition of power/Associative and commutative properties/Definition of multiplication[(2 · x)²+ 2 · 2 · (2 · x) + 4] - [(3 · y)² + 2 · 6 · (3 · y) + 36] + 36 - 68 - 4 = 0 Compatiblity with addition/Definition of multiplication/Commutative and associative properties/(-1) · a = - a(2 · x + 2)² - (3 · y + 6)² - 36 = 0 Perfect square trinomial/Definition of addition4 · (x + 1)² - 9 · (y + 2)² = 36 Compatibility with addition/Existence of additive inverse/Modulative property[tex]\frac{(x+1)^{2}}{3^{2}}-\frac{(y+2)^{2}}{2^{2}} = 1[/tex] Definition of power/Compatibility with multiplication/Existence of multiplicative inverse/ResultThe standard equation of the hiperbola is [tex]\frac{(x+1)^{2}}{3^{2}}-\frac{(y+2)^{2}}{2^{2}} = 1[/tex]. [tex]\blacksquare[/tex]
b) From the result found in a) we conclude that the center of the hyperbola is (h, k) = (-1, -2).
c) The foci of the hyperbola are located at the following two points:
[tex]c = \sqrt{3^{2}+2^{2}}[/tex]
[tex]c = \sqrt{13}[/tex]
F₁ (x, y) = (-1 - √13, -2), F₂ (x, y) = (-1 + √13, -2)
The foci of the hyperbola are F₁ (x, y) = (-1 - √13, -2) and F₂ (x, y) = (-1 + √13, -2). [tex]\blacksquare[/tex]
d) And the asymptotes of the hyperbola are presented below:
y₁ = 2 · x / 3 (2)
y₂ = - 2 · x / 3 (3)
The asymptotes of the hyperbola are y₁ = 2 · (x + 1) / 3 - 2 and y₂ = - 2 · (x + 1) / 3 - 2. [tex]\blacksquare[/tex]
e) The graph of the hyperbola and all its characteristics are presented by means of graphing tool. The result is presented in the image attached below.
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Answer:
The equation of the hyperbola = (x + 1)^2/3^2 - (y + 2)^2/2^2 = 1
The center of the hyperbola = (-1, -2) (h, k)
The vertices of the hyperbola (my assingment asked me for vertices) = (2, -2) and (-4, 2)
The asymptotes = one at y = (2x+2/3) - 2 and the other is at
y = -((2x+2/3) -2)).
Step-by-step explanation:
For the graphing part plug the equation into desm0s and the asymptote equation. For the guiding box part, you use the B variable. Since b = 2 in this problem, you count up two spaces from the center (-1,-2) and then down two spaces. These will be the top and bottom of your guiding box. Then use your vertices as the sides and make a box that connects.
Good luck!
100 POINTS plz dont answer unless you know how to solve this.
Answer:
31.9 mi
Step-by-step explanation:
AC/sin(angleABC) = AB/sin(angleACB)
Find ALL the missing sides and angles of this triangle.
12
40°
A
B
90°
60°
50°
:: 40*
20°
#: 5.3
12
:: 6.4
#: 7.7
:: 9.2
#: 3.6
#: 8.5
Answer:
Step-by-step explanation:
sin40°=[tex]\frac{AC}{12}[/tex]
⇒AC=sin40°×12
⇒AC=7.713≈7.7
cos40°=[tex]\frac{AB}{12}[/tex]
⇒AB=cos40°×12
⇒AB=9.192≈9.2
as A=90°,B=40°
from A+B+C=180°
we can write C=180°-90°-40°
⇒C=50°
What is 5 to the power of zero?
Answer:
1
Step-by-step explanation:
hope this helps, have a great day :)
Answer:
1
Step-by-step explanation:
any number to the power of 0 will equal to 1
[tex] {?}^{0} = 1[/tex]
6+3(13 – 2) - 52
Help me
Answer:
the answer is 14
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the perimeter of the base is 10.4 in and the height of the pyramid is 9.6 in. Round your answer to the nearest tenth of a cubic inch.
9514 1404 393
Answer:
21.6 in³
Step-by-step explanation:
The volume of a square pyramid is given in terms of perimeter and height by ...
V = (1/48)P²h
V = (1/48)(10.4 in)²(9.6 in) ≈ 21.6 in³
The volume is about 21.6 cubic inches.
What is the expression in simplified form?
Answer:
mate what expression
Answer:
what expression?
Step-by-step explanation: