Answer:
17
Step-by-step explanation:
the absolute value function always gives a positive result , that is
| - a | = | a | = a
| - 5 | + | 12 |
= | 5 | + 12
= 5 + 12
= 17
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 surface area of a pyramid with the measurements being 4 4 7
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])
if the discounted price is 14 how much money dose one section represent
The price of one section represent $2.
We will use the tape diagram to represent the sale price and regular price of the item.
We know that percentage is used to represent the fractions of a whole number.
Here, the regular price is the whole number, and the discount and discounted price represent the fractions.
The coupon she used is 30%, which means 30% off the regular price is the discounted price. We know that 30% + 70% = 100%. This means Mia paid 70% of the regular price for the backpack.
Refer to the attached image for the tape diagram.
By looking at the tape diagram attached, it is clear that 7 sections are used to show the discounted price.
If the discounted price is $14,
The price of one section = $14/7 = $2
Therefore, the price of one section is $2.
⇒The regular price = 10 × price of one section = 10 × $2 = $20.
So, Peter needs to pay $20 to buy a similar backpack.
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Disclaimer:
The given question is incomplete.
Assume the following as the complete question.
Mia told Peter that her new backpack only cost $14 because she used a 30% off coupon when she bought it. Peter wants to buy a similar backpack. How much will it cost if he does not have a 30% off coupon?
Wayne ate Takis everyday for n days. He ate 28 bags total.
Write an expression for how many bags of Takis Wayne ate each day.
I NEED AN ANSWER SOON!!!!
The expression for no. of bags of Takis Wayne ate each day is given by, b = 28/n.
What is an expression?Expresssion are mathemaical ways of writing staments.There are many types of mathematical expressions some of them are :- Algebraic expressions, Logarithmic expressions, Trigonometric expressions and many more.
Here the no. of days is represented by 'n' and total no. of bags of akis he ate is 28.
Assuming Wayne ate 'b' bags of Takis everyday.
∴ No. of bags of Takis each day multiplied by no. of days is equal to total no. of bags of Takis he ate which is numerical form is,
b×n = 28.
So, The expression for no. of bags of Takis Wayne ate each day is ,
b = 28/n.
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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°
2. Cassie finishes softball practice at 3:52 p.m. after practicing for 30 minutes. What time did Cassie's
practice start?
Answer:
3:22!
Step-by-step explanation:
Answer:
3:22 p.m.
Step-by-step explanation:
30 minutes before 3:52 p.m.
think of hours and minutes separately for now
3hours
52 minutes
if you are trying to find the time 30 minutes before 3:52 subtract 30 from 52 then put your hours and minutes side by side with a colon (:) in between
3:22
Add a.m. if its after midnight and p.m. if it's after noon
2. Question
A car averages 32 mpg. Gas costs $1.97 per gallon. How much
would it cost to pay for the gas if this car made a trip of 866 miles?
O$37.51
O$13.73
0 $55.20
O$53.31
show
your
Work ↓
The cost for 866 miles will be $53.31.
How to calculate the cost?The car car averages 32 mpg and gas costs $1.97 per gallon.
Therefore,. the cost for 866 miles will be:
= 866/32 × $1.97
= 27.0625 × $1.97
= $53.31
The cost is $53.31.
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In right triangle abc with m/C=90°, m/B=75°, and AB = 12 cm. Find the area
of triangle ABC. No trig
The area of the Triangle ABC will be 18 cm²
In the question, It is given that ∠B = 75° and ΔABC is Right angeled at ∠C = 90° and AB = 12CM.
We know that the Area of Δ is defined by : [tex](\frac{1}{2} *b*h)[/tex]
In the picture below, we have base and height BC and AC respectively.
We don't have the values for AC and BC. So to find the values of Base & Height we will use Trigonometric Ratios.
We know Sin(∠) = Perpendicular/Hyoptenuse and,
Tan(∠) = Perpenciular/Base. Putting values into the respective ratios and taking ∠B = 75°, we get
=> [tex]Sin(B) = \frac{AC}{BC} = > Sin(75) = \frac{AC}{12}[/tex]
=> [tex]AC = 0.96 * 12 = > AC = 11.59[/tex]
Similarly, [tex]Tan(B) = \frac{AC}{BC} = > Tan(75) = \frac{11.59}{BC}[/tex]
=> [tex]BC = \frac{11.59}{3.73} = > BC = 3.10[/tex]
Now, we have AC = 11.59cm and BC = 3.10cm putting these values in the Area of the Triangle we get :
Area = [tex]\frac{1}{2} *b*h[/tex] => Area = [tex]\frac{1}{2}[/tex] * BC * AC
Area = [tex]\frac{1}{2}[/tex] * 3.10 * 11.59 => Area = 18
Hence, we get the Area of Δ ABC = 18cm²
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Answer:
18
Step-by-step explanation:
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.
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
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 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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If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?
Answer:
0.05
Step-by-step explanation:
Answer:
10 cents
Step-by-step explanation:
Well the bat and baseball is 1.10 simply subtract 1.00 from 1.10 and you have your answer!
Have an AMAZING day! :)
(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]-
An ice cream store recorded the flavors of its recent cone sales.
chocolate 10
cookie dough 6
mocha 20
vanilla 8
Considering this data, how many of the next 99 cones sold would you expect to have mocha ice cream?
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
(3.85 x 103) - (1.4 x 102) In scientific notation I need ASAP plss
Answer:
Step-by-step explanation:
x^10
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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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 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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explain the process of finding the mean of a data set in your own words.
Answer:i hope this helps
Step-by-step explanation:add all the terms together and divide by the amount of terms given
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]
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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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
x=17/99
Step-by-step explanation:
Lets break this problem down ^^
Let x= 0.171717...
100x = 17.1717...
100x=17.1717.. - x=0.171717...
99x=17
x= 17/99
Hope this helps!! ^^
hlllppppp! brainliest to first
y = -2x + 18
y = 8
Solution for the above system?
brainliest to first!!!!!!!hlpppppp!!!!!!!!!!!
Answer:
x =5
Step-by-step explanation:
8 = -2x + 18 Subtract 18 from both sides
-10 = -2x Divide both sides by -2
5 = x
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:
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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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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Convert the following recurring decimals to fractions
0.617