Answer:
(a,b)
Step-by-step explanation:
Using the Midpoint formula,
[tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
you will get
[tex]\left(\frac{2a+0}{2},\:\frac{0+2b}{2}\right)[/tex]
which is
(a,b)
Chelsea wants to rearrange her room. She makes a scale drawing of the room and cuts out pieces of paper to represent her furniture. The paper representing her desk is 1 1/4 inches by 2 1/4 inches. What are the actual dimensions of her desk?
A: 1 3/4 feet by 3 feet
B: 2 1/2 feet by 5 feet
C: 2 1/4 feet by 4 1/4 feet
D: 2 1/2 feet by 4 1/2 feet
Since the paper representing her desk is 1 1/4 inches by 2 1/4 inches, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft
To answer the question, we need to know what scale is
What is a scale?A scale is the ratio of two dimension and it is given on a scale drawing.
Given that Chelsea makes a scale drawing of the room and cuts out pieces of paper to represent her furniture, and the paper representing her desk is 1 1/4 inches by 2 1/4 inches.
Since on the scale, we have 1/2 in = 1 foot ⇒ 1 in = 2 ft
Actual dimensions of deskSo, the actual dimensions of her desk are
1 ¹/₄ in by 2 ¹/₄ in = 5/4 in by 9/4 in
= 5/4 × 1 in by 9/4 × 1 in
= 5/4 × 2 ft by 9/4 × 2 ft
= 5/2 ft by 9/2 ft
= 2 ¹/₂ ft by 4 ¹/₂ ft
So, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft
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The sun of two numbers is 7 and a different 1 what are the two numbers
Answer:
3 and 4
Step-by-step explanation:
given that the difference is 7, two numbers that add up to 7 are 3 and 4.
Change 24 inches into feet given the fact that 1 foot = 12 inches.
Answer:
2 feet
Step-by-step explanation:
1 foot = 12 inches
2 feet=24 inches
Answer:
2 feet
Step-by-step explanation:
12 x 2 is 24.
Round of to the nearest thousand 741,543
Answer:
The correct answer is 742,000
Step-by-step explanation:
Answer:
742,000
Step-by-step explanation:
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HELP ASAP!! ANSWER QUESTION IN PICTURE BELOW!!!
Answer:
a
Step-by-step explanation:
anything less than 18 is wrong
A rectangular piece of iron has sides with lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3 m. what is the volume of the piece of iron? 6.96 × 10–7 m3 6.96 × 107 m3 6.96 × 10–18 m3
The volume of the rectangular piece with sides of lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3m is 6. 96 × 10^ -7 m
What is volume?Volume is defined as the amount of space or capacity occupied by a three-dimensional shape.
It is represented in cubic units.
How to determine the volume of a rectangleFormula:
Volume, V = length × breadth × height
Given the values;
7. 08 × 10 ^-3m , 2.18 × 10^ -2m and 4. 51 × 10^-3m
Multiply all the lengths
Volume = 7. 08 × 10 ^-3 × 2.18 × 10^ -2 × 4. 51 × 10^-3
= 69.6 × 10^-8
= 6. 96 × 10^ -7 m
Therefore, the volume of the rectangular piece is 6. 96 × 10^ -7 m
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Answer:
A
Step-by-step explanation:
trust
An investment of $2,375 is made in a 7-year cd that earns 314% annual interest that is compounded continuously. how much will the cd be worth at the end of the 7-year term? round your answer to the nearest cent. do not include the dollar sign.
The worth of the cd at the end of 7 years will be $384,101.79.
What will be the worth of the investment?When an investment earns an interest that is compounded continuously, it means that it earns interest continuously.
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate2375 x (e^3.14) x 7 = $384,101.79
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-33 + 8x = -3 (3x+6) + 2
Answer:
x = 1
Step-by-step explanation:
-33 + 8x = -9x - 18 + 2
8x+ 9x = -18 + 2 + 33
17x = -16 + 33
17x = 17
x = 1
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The functions f and g are defined as follows.
f(x)=2x²-3x
g(x) = -4x-1
Find f(-2) and g (7).
Simplify your answers as much as possible.
f(-2) =
믐
X
9 (7) =
Ś ?
Answer:
f(-2) = -14g(7) = -29Step-by-step explanation:
~1
Given Polynomial:
f(x)=2x²-3xTo Find:
f(-2)Solution:
f(x)=2x²-3xSubstitute x = -2 onto the given polynomial,as we need to find f(-2),so x = -2.
f(6) = 2(-2)² -3(-2)Simplify using PEMDAS,then.
f(6) = -8 - 6f(6) = -14Hence, f(6) = -14
[tex] \rule{225pt}{2pt}[/tex]
~2
Given polynomial:
g(x) = -4x-1To Find:
g(7)Solution:
g(x) = -4x-1
Substitute x = 7 onto the given polynomial,as we need to find g(7),so x = 7.
g(7)= -4(7) - 1Simplify using PEMDAS.
g(7) = -28 - 1g(7) = -29Hence, g(7) = -29.
[tex] \rule{225pt}{2pt}[/tex]
7) Heather records the number of winners of the three Ring Toss game in the table below.
Number of Number of
Players
Winners
Game 1
123
52
Game 2
155
63
Game 3
172
65
Based on the data recorded in the table, how many winners should Heather expect if there
are 750 players?
The number of winners that Heather can expect is 300.
How many winners can be expected?The first step is to determine the total number of winners to the total number of players using the information in the table.
Total number of winners = 52 + 63 + 65 = 180 Total number of players = 123 + 155 + 172 = 450Ratio = 180 / 450 = 0.40
Number of winners if there are 750 players = 0.40 x 750 = 300 winners
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Find the 50th term of the sequence: 65536,49152,36846,27648
Step-by-step explanation:
first you should check whether the sequence is arithmetic and geometric .as you see the sequence is arithmetic with the common difference of -16384.
Jayne Stopped to get gas before going on a road trip the tank already had 4 gallons of gas in it which equation relates the total amount of gasoline in the tank y to the number of gallons that she put in the tank X
a.) y=4+x
b.) y = x - 4
c.) y = 4 . x
d.) y = x / 4
Answer: A.) y=4+x
Step-by-step explanation:
IM SO LOST PLS HELP ME
[tex]~~~~~~~c = \dfrac{a^2 +3b}{4}\\\\\implies 4c = a^2 +3b\\\\\implies 3b = 4c-a^2\\\\\implies b = \dfrac{4c-a^2}{3}[/tex]
Answer:
b = [tex]\frac{(4c-a^2)}{3}[/tex]
Step-by-step explanation:
[tex]c=\frac{a^{2}+3b }{4}[/tex]
First, let us multiply both sides by 4.
4c = a² + 3b
Now let us take a² to the left side.
4c - a² = 3b
Now to make b as the subject let us divide both sides by 3.
[tex]\frac{(4c-a^2)}{3} =\frac{3b}{3}[/tex]
Therefore,
b = [tex]\frac{(4c-a^2)}{3}[/tex]
What is the first step in the solution of 3x2+6x=12 by completing the square?
A: r3+r=2
B: r2+2r=4
C: 3r2+6r+9=12+9
D: 3r2+6r+36=12+36
Answer:
B: r² + 2r = 4
Explanation:
[tex]\rightarrow \sf 3x^2+6x=12[/tex]
divide both sides by 3
[tex]\rightarrow \sf x^2+2x=4[/tex] ← This is the result of the first step.
factor out the common term
[tex]\rightarrow \sf x(x+2) = 4[/tex]
set to 0
[tex]\rightarrow \sf x = 4, \ x+2 = 4[/tex]
simplify
[tex]\rightarrow \sf x = 4, \ x= 2[/tex]
Divide all terms by a i.e 3
We get
x²+2x=4Or
r²+2r=4Option B is correct
Write an equation of the parabola in vertex form that passes through ( 3 , -2 ) and has a vertex of ( 5,8 )
Answer:
Parabola in vertex form: y = a(x - h)2 + k
Vertex: (h, k) = (3, 2) and (x, y) = (13, 8)
y = a(x - h)2 + k
y = a(x - 3)2 + 2 <== with substitution (h, k) = (3, 2)
8 = a(13 - 3)2 + 2 <== with substitution (x, y) = (13, 8)
8 = a(10)2 + 2
100a = 8 - 2 ==> 100a = 6 ==> a = 6/100 ==> a = 3/50
Parabola in vertex form: y = a(x - h)2 + k
y = (3/50)(x - 3)2 + 2 (Final Answer - Parabola in vertex form)
Step-by-step explanation:
Answer:
Hi,
Step-by-step explanation:
Parabola has the equation:
y=k*(x-5)²+8
if x=3, y=-2: -2=k*(-2)²+8 ==> 4k=-10==> k=-5/2
So y=-5/2(x-5)²+8
write Six times a number w is at least -24 as an inequality
Answer:
[tex]6n \geq -24[/tex]
Step-by-step explanation:
First let's provide a variable for "a number" and call it [tex]n[/tex].
So "six times a number" could be written as [tex]6*n[/tex].
"Is at least" in mathematical terms means "greater than or equal to" or
≥
Putting this altogether gives the expression:
[tex]6n\geq -24[/tex]
What is the value of the expression when n = 3?
6 (n² + 2)
n
O 16
O22
O 30
O 66
Answer:
66
Step-by-step explanation:
6(n² + 2)
6(3² + 2)
6(9 + 2)
6(11)
66
A giant pie is created in an attempt to break a world record for baking. The pie is shown below: What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
78.13 ft
82.43 ft
86.31 ft
91.98 ft
if the "d"iameter of the pie is 30, then its radius must be half that, or 15.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =42 \end{cases}\implies \begin{array}{llll} A=\cfrac{(42)\pi (15)^2}{360}\implies A=\cfrac{105\pi }{4} \\\\\\ \stackrel{using~\pi =3.14}{A\approx 82.43} \end{array}[/tex]
Anthony shines a beam of light on the surface of a solution of glycerol at a certain angle. if the angle of refraction is 38°, what is the angle of incidence? the index of refraction of glycerol is 1.47, while that of air is 1.00. a. 38° b. 45° c. 55° d. 65° e. 70°
Answer:
D) 65°
Step-by-step explanation:
Use Snell's Law
[tex]n_1\sin\theta_1=n_2\sin\theta_2\\\\1.00\sin\theta_1=1.47\sin38^\circ\\\\\sin\theta_1=1.47\sin38^\circ\\\\\theta_1=\sin^{-1}(1.47\sin38^\circ)\\\\\theta_1\approx64.83^\circ[/tex]
Thus, the angle of incidence is D) 65°
Pippa has a box containing n pens.
there are only black pens and red pens in the box.
the number of black pens in the box is 3 more than the number of red pens.
pippa is going to take at random 2 pens from the box.
the probability that she will take a black pen followed by a red pen is
9
35
find the possible values of n.
show clear algebraic working.
The possible values of N from the given probability parameters is; N equals 15 or 21
How to Solve Algebra Problems?We are told that;
Number of pens in the box = N
Let the number of red pens be x
Thus; number of black pens = x + 3
Thus;
x + x + 3 = N
x = (N - 3)/2
The probability that she will take a black pen followed by a red pen is;
P(she will take a black pen followed by a red pen) = (x + 3)/N * x/(N - 1)
Plugging in he relevant values and solving for N gives ;
Solving for N gives N equals 15 or 21
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Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with outward normal orientation away from the origin
Parameterize S by the vector function
[tex]\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle[/tex]
with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.
Compute the outward-pointing normal vector to S :
[tex]\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle[/tex]
The integral of the field over S is then
[tex]\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}[/tex]
My age this year is a multiple of 7. Next year it will be a multiple of 5. I am more than 20 years of age but less than 80. How old will I be 6 years from now?
Answer:
You will be 55
Step-by-step explanation:
Nevaeh models the volume of a popcorn box as a right rectangular prism. Its dimensions are 5 in by 3 in by 7 1/4 in. How many cubic inches of popcorn would it hold when it’s a quarter full? Round your answer to the nearest tenth if necessary.
The cuboid can hold 27.2 cubic inches of popcorn
What is a right rectangular prism?A right rectangular prism is also called the cuboid. it is a solid three dimensional shape with 6 faces, 12 edges and 8 vertices.
Analysis:
Volume of cuboid = length x width x height
= 5 x 3 x 29/4 = 108.75 cubic inches
When it is quarter full, volume = 1/4 x 108.75 = 27.2 cubic inches
In conclusion, the volume of the cuboid is 27.2 cubic inches.
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Help me if you can please!!!
To solve this, we need to use our trigonometric equations:
⇒ look at the diagram attached
Let's examine what the problem wants:
the length of the side opposite to the 27-degree angleLet's examine what the problem gives us:
the length of the side adjacent to the 27-degree anglethe angle that has a measure of 27-degreesLet's solve:
[tex]tan(27)=\frac{x}{15} \\x=15*tan(27)\\x=7.64[/tex]
Answer: 7.6 (rounded to the nearest tenth)
Hope that helps!
Solve the formula for a linear equation, y = mx + b, for m. I’m not so great at formulas and it’d be great if someone helped thank you :)
Answer:
See below
Step-by-step explanation:
mx + b = y subtract 'b' from both sides of the equation
mx = y - b now, divide both sides by 'x'
m = (y-b)/x
Find the measure of the missing angle.
112°
a
The measure of angle b is 112° and the measure of angle c is 68°
Calculating the measures of anglesFrom the question, we are to determine the measures of the missing angles
From the diagram,
b = 112° (Vertically opposite angles)
∴ b = 112°
Also,
112° + c = 180° (Sum of angles on a straight line)
c = 180°- 122°
∴ c = 68°
Hence, the measure of angle b is 112° and the measure of angle c is 68°
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elo guys can u guys help me on these i have 20 min
I used exemplar. the mean means add all the numbers and divide it buy how many there are.
5 + 7 + 9 = 21
21/3 = 7
0 3 4 6 6 7 7 7 9
Median = 6 (the middle number)
Mode = 7 (the most common number)
Range = 9 (Biggest number - smallest number)
Hope this helps!
If not then let me know!
Find the minimum point(s) of f(x) = x - 2x² + 1 given that f'(x) = 4x³ - 4x.
Answer: f(x) = x - 2x² + 1
x=-b/2a
(1/4,9/8
2. f'(x) = 4x³ - 4x
((\sqrt(3))/(3),-(8\sqrt(3))/(9))is a local minima
(-(\sqrt(3))/(3),(8\sqrt(3))/(9))is a local maxima
Step-by-step explanation: hopes this help
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Denise is designing the seating arrangement for a concert at an outdoor theater. to give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. explain to denise how to create an equation to predict the number of seats in any row. then, using your equation, show your work to determine the number of seats in row 18
An equation is formed of two equal expressions. The number of seats in row 18 will be 119.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A.) Given the number of seats that the first row can have is 11, while the number of seats that the next row should have is six more than the previous one. Therefore, the number of seats will increase linearly.
Thus, the equation for the number of seats in any row can be given as y=11+6x, where y is the number of seats and x is the number of row.
B.) The number of seats in row 18 will be equal to,
y = 11 + 6x
y = 11 + 6(18)
y = 11 + 108
y = 119
Hence, the number of seats in row 18 will be 119.
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A cone has a height of 9 feet and a radius of 8 feet. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
please help me i dont get it. :(