Answer:
y = - 5x - 7
Step-by-step explanation:
A line has a function:
y = ax + b
Because the line has a slope of - 5
=> a = - 5
=> y = - 5x + b
Because the line goes through point (- 1; - 2)
=> - 2 = (- 5).(- 1) + b
=> 5 + b = - 2
=> b = - 7
=> The slope intercept from of the line:
y = - 5x - 7
3x + 4y = -23
2y - x = -19
What is the solution (x, y) to the system of equations
above?
A) (-5,-2)
B) (3, -8)
C) (4, -6)
D) (9,-6)
=======================================================
Explanation:
I'll use the substitution method.
Let's solve the second equation for x.
2y - x = -19
-x = -19-2y
x = 19+2y
Then plug that into the first equation
3x + 4y = -23
3( x ) + 4y = -23
3(19+2y)+4y = -23
3*19 + 3*2y + 4y = -23
57+6y+4y = -23
57+10y = -23
10y = -23-57
10y = -80
y = -80/10
y = -8
Use this y value to find x.
x = 19+2y
x = 19+2(-8)
x = 19-16
x = 3
---------------------------
Summary:
We found that x = 3 and y = -8
The ordered pair solution is therefore (x,y) = (3, -8)
Technically you could have stopped once reaching y = -8, since choice B is the only one that fits the description. But it helps to have practice.
Answer:
answer is B
Step-by-step explanation:
picture is upside down.
Fill in the missing parts in the equivalent forms:
6/9 = blank/6
Answer:
9
Step-by-step explanation:
Find the distance between A (4, 6) and B (9, 7). Write your answer as a radical and as a decimal rounded to the nearest
tenth.
The distance between the two points is ___ or about ___
Answer: the distance between the two points is √26 or about 5.1
Step-by-step explanation:
A(4,6) B(9,7)
[tex]\boxed {L_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} }\\\\L_{AB}=\sqrt{(9-4)^2+(7-6)^2} \\\\L{ab}=\sqrt{5^2+1^2}\\\\ L_{AB}=\sqrt{25+1} \\\\L_{AB}=\sqrt{26} \\\\L_{AB}\approx5.1[/tex]
The distance between A (4, 6) and B (9, 7) is √26 or 5.1.
How to find the distance between two points?Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So the distance between A (4, 6) and B (9, 7) will be
[tex]d = \sqrt {\left( {4 - 9 } \right)^2 + \left( {6 - 7 } \right)^2 }[/tex]
d = √26 = 5.099
Rounded to nearest tenth ⇒ 5.1 units.
Hence "The distance between A (4, 6) and B (9, 7) is √26 or 5.1".
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Two trains leave stations 504 miles apart at the same time and travel toward each other. One train travels 95 at miles per hour while the other travels at 85 miles per hour. How long will it take for the two trains to meet? Do not do any rounding.
Answer:
Step-by-step explanation:
12312ejljaslkjkfdsjkdsfafsd
3 and 1/4 divided by 2 and 1/6
Answer:
{3 1/4} / {2 1/6} =
1.5
Step-by-step explanation:
Answer:
Exact Form:
3/2
Decimal Form:
1.5
Mixed Number Form:
1 1/2
the base of s is the triangular region with vertices (0, 0), (2, 0), and (0, 2). cross-sections perpendicular to the x-axis are squares.
I assume you want the volume of the shape with the given cross sections. In the [tex]x,y[/tex]-plane, the base is set
[tex]\left\{(x,y) ~:~ 0\le x\le 2 \text{ and } 0 \le y \le 2-x\right\}[/tex]
Each cross section is a square plate with side length [tex]2-x[/tex] (the vertical distance between the [tex]x[/tex]-axis and the line [tex]y=2-x[/tex]) and thickness [tex]\Delta x[/tex], hence volume [tex](2-x)^2\,\Delta x[/tex].
As [tex]\Delta x\to0[/tex] and the number of cross sections grows to infinity, the total volume of the plates converges to volume of the solid [tex]S[/tex], given by the definite integral
[tex]\displaystyle \int_0^2 (2-x)^2 \, dx = \int_0^2 x^2 \, dx = \frac{2^3-0^3}3 = \boxed{\frac83}[/tex]
(where we make the substitution [tex]2-x\mapsto x[/tex])
how to solve this with steps?
Answer:
you don't
Step-by-step explanation:
this is at it's simplest form, tell your teacher that or if its online answer, talk to your tutor or teacher
5:43 pm ----What is 1 hour and 30 minutes more of this? (I mean, what time will it be?)
Answer:
7:13
Step-by-step explanation:
5:43
1 hour from 5:43 will be 6:43
17 mins from 6:43 will be 7:00
13 mins from 7:00 will be 7:13
Please help! Radicals.
(Check pics)
Answer:
[tex] - 26 \sqrt{10} [/tex]
Step-by-step explanation:
Simplify.
[tex] \rightarrow \sqrt{40} \: \: \: \: \: \: \: \: \\ = \sqrt{4 \times 10} \: \: \: \\ = \sqrt{4} \times \sqrt{10} \\ = 2 \times \sqrt{10} \: \: \: \: \\ = 2 \sqrt{10} \: \: \: \: \: \: \: \: \: [/tex]
[tex] \rightarrow \sqrt{160} \\ = \sqrt{16 \times 10} \: \: \: \\ = \sqrt{16} \times \sqrt{10} \\ = 4 \sqrt{10} \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Let us solve the given expression now.
[tex] - \sqrt{40} - 6 \sqrt{160} \\ - 2 \sqrt{10} - 6 \times 4 \sqrt{10} \\ - 2 \sqrt{10} - 24 \sqrt{10} \\ - 26 \sqrt{10} [/tex]
find the direction cosines and direction angles of the vector. (give the direction angles correct to the nearest tenth of a degree.)
The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are
cosα = x/r = 3√2/10cosβ = y/r = 4√2/10 and cosγ = z/r = √2/2So, the direction angles are
α = cos⁻¹(x/r) = cos⁻¹(3√2/10) = 64.9°β = cos⁻¹(y/r) = cos⁻¹(4√2/10) = 55.6° and γ = cos⁻¹(z/r) = cos⁻¹(√2/2) = 45°How to find the direction cosines and direction angles of the vector?Given a vector r = xi + yj + zk where
x, y and z are the components of the vector in the x, y and z directions. and r = √(x² + y² + z²)The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are
cosα = x/r, cosβ = y/r and cosγ = z/rSo, their direction angles are
α = cos⁻¹(x/r), β = cos⁻¹(y/r) and γ = cos⁻¹(z/r)As an example, let r = 3i + 4j + 5k
So, r = √(x² + y² + z²)
= √(3² + 4² + 5²)
= √(9 + 16 + 25)
= √50
= 5√2
The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are
cosα = x/r = 3/5√2 = 3√2/10cosβ = y/r = 4/5√2 = 4√2/10 and cosγ = z/r = 5/5√2 = 1/√2 = √2/2So, the direction angles are
α = cos⁻¹(x/r) = cos⁻¹(3√2/10) = cos⁻¹(0.4243) = 64.9°β = cos⁻¹(y/r) = cos⁻¹(4√2/10) = cos⁻¹(0.5657) = 55.6° and γ = cos⁻¹(z/r) = cos⁻¹(√2/2) = cos⁻¹(0.5657) = 45°Learn more about direction cosine here:
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what is the area of rectangle wxyz with vertices wleft-parenthesis 0 comma 1 right-parenthesis, xleft-parenthesis 3 comma 4 right-parenthesis , yleft-parenthesis negative 1 comma 8 right-parenthesis, zleft-parenthesis negative 4 comma 5 right-parenthesis to the nearest unit?
The area of the rectangle will be 24sq, units.
How can we calculate the area of the rectangle?To determine the area of various polygons, there exist specialized formulae. The general formula for rectangles is as follows:
A = width x length
Given, the coordinates of the rectangle are W(0,1), X(3,4), Y(-1, 8), Z(-4,5)
So the length of rectangle will be = distance between W and X will be -
⇒[tex]\sqrt{(3 - 0)^{2} + (4-1^{2}) }[/tex]
⇒[tex]\sqrt{18}[/tex]
The breadth of rectangle will be = distance between X and Y
⇒ [tex]\sqrt{(3 + 1)^{2} + (8-4)^{2} }[/tex]
⇒ [tex]\sqrt{32}[/tex]
Now, area of rectangle = length × breadth
⇒ [tex]\sqrt{18}[/tex] × [tex]\sqrt{32}[/tex]
⇒ 24 sq. units
So, the area of the rectangle will be - 24 sq. units
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a builder wants to install hardwood flooring in a dining room of length 8.68 m and width 6.1 m. what is the area of the room (in m2)?
Answer:
52.948 m²
Step-by-step explanation:
→ State the formula for the area
length × width
→ Substitute in the numbers
8.68 × 6.1 = 52.948 m²
In 34,65/2,31,59/2 which term is 16?
Answer:
8
Step-by-step explanation:
Answer:
none is
Step-by-step explanation:
Find the measure of the missing angles.
121°
20°
e
d
f
Answer: e=20° d=121° f=39°
Answer:
f=39°
e=20°
d=121°
Step-by-step explanation:
d=121°(vertically opposite angles are equal)
e=20°(vertically opposite angles are equal)
f=180°-(d+e)
=180-141
=39°
(3.85 x 103) - (1.4 x 102) In scientific notation I need ASAP plss
Answer:
Step-by-step explanation:
x^10
math work please help <3
Using translation concepts, it is found that:
a.
The equation is: y = -1.5(x + 4)² + 9.The domain is all real values.The range is y ≤ 9.b.
The rule is [tex]y = -\sqrt{x + 5} + 10[/tex].The domain is x ≥ -5.The range is y ≤ 10.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Quadratic functionThe quadratic function has vertex at (-4,-6), hence:
y = a(x + 4)² - 6
When x = -6, y = 0, hence we use it to find a as follows:
0 = 4a - 6
a = 1.5.
Hence the function is:
y = 1.5(x + 4)² - 6.
When it is reflected over the x-axis, we have that:
y -> -y.
Hence:
y = -1.5(x + 4)² + 6.
When it is moved up 3 units, we have that y -> y + 3, hence:
y = -1.5(x + 4)² + 9.
The function is defined for all real values, assuming values from negative infinity to 9, hence:
The equation is: y = -1.5(x + 4)² + 9.The domain is all real values.The range is y ≤ 9.Square root functionThe parent square root function is given by:
[tex]y = \sqrt{x}[/tex]
From the graph, it is found that:
The function was reflected over the x-axis, hence y -> -y.The function was shifted one unit to right, hence x -> x - 1.The function was shifted two units up, hence y -> y + 2.Hence the rule is:
[tex]y = -\sqrt{x - 1} + 2[/tex]
The translations given by the item are:
6 units left, hence x -> x + 6.8 units up, hence y -> y + 8.Thus:
[tex]y = -\sqrt{x + 5} + 10[/tex]
Then the function will be defined for values of -5 and greater, assuming values of 10 and less, hence:
The rule is [tex]y = -\sqrt{x + 5} + 10[/tex].The domain is x ≥ -5.The range is y ≤ 10.More can be learned about translation concepts at https://brainly.com/question/4521517
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Find. 5.3 • 10 to the power of 3 - 8 • 10 to the power of 2.
Express you answer in scientific notation
Answer: 568000
Step-by-step explanation:
the table shows the total cost of different numbers of square feet of carpet.
what is the rate of change in dollars with respect of the number of square feet purchased for this linear relationship
The rate of change is $7 per one square feet.
What is the rate of change?In order to determine the rate of change, the difference between each successive cost would be divided by the difference in each successive size.
Rate of change = change in cost /change in size
(980 - 840) / (140 - 120)
140 / 20
= $7
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can anyone help with
4x + 6 + 2x = 18
Answer:
x=2
Step-by-step explanation:
[tex]4x+2x+6=18 < - Start-by-grouping-the-like-terms![/tex]
[tex]6x+6=18 < - Then-add-the-similar-elements![/tex]
[tex]6x+6-6=18-6 < - Subtract-6-from-both-sides-and-simplify.[/tex]
[tex]6x=12[/tex]
[tex]\frac{6x}{6}=\frac{12}{6} < - Divide-both-sides-by-6-to-further-simplify![/tex]
[tex]x=2[/tex]
________________________________________________________
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Solve the following equation.
(90-x)-x=18
Answer:
x = 36
Step-by-step explanation:
In the figure below, m1=8x° and m2 = (x-9)°.
Find the angle measures.
1
1 2
Answer:
<1 = 168
<2 = 12
Step-by-step explanation:
First, you need to solve for x
8x + x -9 = 180
9x -9 = 180
9x = 189
x = 21
Now, substitute in 21 for x for both angles
8(21) = 168
(21) - 9 = 12
find the volume of the parallelepiped with one vertex at (5,4,4), and adjacent vertices at (0,−1,5), (4,10,5), and (11,7,11).
The volume of the parallelepiped is 299³ units.
What is parallelepiped?A parallelepiped is a three-dimensional character formed by six parallelograms in geometry (the term rhomboid is also sometimes used with this meaning). It is analogous to a parallelogram in the same way that a cube is analogous to a square. In Euclidean geometry, the 4 concepts—parallelepiped and cube in three dimensions, parallelogram as well as square in two-dimension —are defined, but only parallelograms and parallelepipeds exist in the context of more general affine geometry, in which angles are not differentiated.So,
The volume of parallelopiped can be calculated using the steps below.
PQ = Q - Vertex = (-5, -5, 1)PR = R - Vertex = (-1, 6, 1)PS = S - Vertex = (6, 3, 7)Now, the volume of parallelopiped is increasing:
[tex]v=\left|\begin{array}{lll}-5 & -5 & 1 \\-1 & 6 & 1 \\6 & 3 & 7\end{array}\right|[/tex]
The matrix's determinant is:
⇒ -5(42 - 3) +5(-7 -6) +1(-3 - 36)
⇒ -5(39) +5(-13) +1(-39)
⇒ -195 -65 -39
⇒ |-299| = 299
Therefore, the volume of the parallelepiped is 299³ units.
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is 47.2 greater than 47.197?
Answer:
Yes.
Step-by-step explanation:
Think of it this way,
0.2 = 200
0.197 = 197
200 > 197
PLSSS HELP IF YOU TURLY KNOW THISS
1. If AJKL APQR, which one of these is not a pair of corresponding parts?
What is the surface area of a pyramid with the measurements being 4 4 7
Convert the following recurring decimals to fractions
0.617
The radius of a cone can be found using the formula , where stands for the volume of the cone and stands for the height. If r=3, h=6, and pi is 3.14 , find the volume (V). Round the answer to the nearest hundredths place.
The volume of the cone with radius 3 and height of the cone 6 is 56.52.
Any shape's volume in geometry is the area it takes up in a three-dimensional space. As a result, the space occupied by a cone in three dimensions is known as its volume.
The formula for the radius of a cone is given as:
r = √( 3 × V / π × h)
Where h is the height of the cone, V is the volume of the cone.
Now, squaring the above equation.
(r)² = [ √( 3 × V / π × h) ]²
r² = [ √ (3 × V) / √ ( π × h ) ]²
3V = π × r² × h
V = π × r² × h / 3
We have,
r = 3, h = 6, and π = 3.14
V = ( 3.14 × (3)² × 6 / 3 )
V = 3.14 × 3 × 6
V = 56.52
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(1 point) Find an equation for the linear function g(x) which is perpendicular to the line 5x−2y=6 and intersects the line 5x−2y=6 at x=8.
g(x)=
Answer: y=-0.4x+20.2
Step-by-step explanation:
[tex]5x-2y=6\\5x-2y+2y=6+2y\\5x=6+2y\\5x-6=6+2y-6\\5x-6=2y[/tex]
Divide both parts of the equation by 2:
[tex]\displaystyle\\\frac{5x-6}{2}=y\\\\\frac{5}{2} x-3=y[/tex]
Coordinates of the intersection point of the equations:
[tex]\displaystyle\\y=\frac{5}{2}x-3 \ and\ x=8\ are:[/tex]
[tex]\displaystyle\\x=8\\Hence,\\y=\frac{5}{2} (8)-3\\\\y=\frac{5*8}{2} -3\\\\y=\frac{5*4*2}{2}-3\\\\y=5*4-3 \\\\y=20-3\\\\y=17\\Thus, (8,17)[/tex]
[tex]\displaystyle\\The\ slope\ \perp=-\frac{1}{\frac{5}{2} } \\\\The\ slope\ \perp=-\frac{2}{5}[/tex]
[tex]\displaystyle\\-\frac{2}{5} =\frac{y-17}{x-8}[/tex]
Multiply both parts of the equation by (x-8):
[tex]\displaystyle\\-\frac{2}{5}(x-8)=y-17\\\\-\frac{2}{5} x+\frac{2*8}{5} =y-17\\\\-\frac{2}{5}x+\frac{16}{5} =y-17\\\\ -0.4x+3.2=y-17\\\\ -0.4x+3.2+17=y-17+17\\\\-0.4x+20.2=y[/tex]-
abigail wanta to find three consecutive even integers whose sum is four times the smallest of those integers. she lets n represent the smallest integer, then writes this equation n + (n + 2) + (n + 4) = 4n
Step-by-step explanation:
first add all the n together
3n and 4n
add those together too
7n
now add 2+4
6 now
7n\-7n =6/-7n = -1n