[tex]\begin{cases} u=6i-2j\\\\ v=-3i+7j \end{cases}\qquad \begin{cases} < 6~~,~~-2 > \\\\ < -3~~,~~7 > \end{cases} \\\\[-0.35em] ~\dotfill\\\\ u-v\implies < 6~~,~~-2 > ~~ - ~~ < -3~~,~~7 > \\\\\\ < 6-(-3)~~,~~-2-7 > \implies < 6+3,-9 > \implies < 9,-9 > \implies 9i-9j[/tex]
A rectangular piece of metal is 10 in longer than it is wide. Squares with sides 2 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1102in^3, what were the original dimensions of the piece of metal?
The length and width of the piece of metal are 20 and 30 inches respectively.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Dimension of the rectangle;
Width(w)
Length,L= 10 + w
volume of the box = length * width * height
Dimension of the box;
length of box, (x + 10) - 4 = x + 6
width of box,(x - 4)
height of box = 2
The volume of the box is 1102 in³;
⇒V=lwh
⇒V=2 (x -4)( x + 6) =
⇒1102 in³ = 2x² + 4x - 48
⇒2x² + 4x - 880 = 0
⇒x + 2x - 440 = 0
⇒(x + 22)(x - 20) = 0
⇒x = 20
⇒x=-22 (value of the dimesion will not be negative.
The width of an original piece of metal is;
Width,w=20 inches
length,l= 30 inches
Hence. the length and width of the piece of metal are 20 and 30 inches respectively.
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9.8765 plus what has a 10 in the front
Answer:
0.1235
Step-by-step explanation:
I'm not exactly sure what you mean, but I'm guessing that it's how much is needed to get 10 as the whole number. In that case, you just do 10-9.8765 to get 0.1235. So, 9.8765+0.1235=10. Hope this helped!
What is the approximate radius of a sphere with a volume of 113 cm3?O A. 3 cm O B. 4 cm O c. 2 cm O D. 5 cm
Considering it's volume of 113 cm³, the approximate radius of the sphere is given by:
A. 3 cm
What is the volume of an sphere?
The volume of an sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, we have that V = 113 cm³, hence the radius in cm is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
[tex]113 = \frac{4\pi r^3}{3}[/tex]
[tex]r^3 = \frac{113 \times 3}{4\pi}[/tex]
[tex]r = \sqrt[3]{\frac{113 \times 3}{4\pi}}[/tex]
r = 3 cm.
Hence option A is correct.
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Answer:
is 3 cm
Step-by-step explanation:
Which of the following fraction pairs is equivalent?
12/20 and 20/25 18/27 and 10/15 6/24 and 5/15 3/25 and 5/25
Answer:
b
Step-by-step explanation:
answer is b
Drag one comparison statement into each box below to make a true statement. Each comparison statement may be used once, more than once, or not at all.
The inequalities are; 5¹/₄ tons = 10500 pounds; 1/2 ton + 3/4 ton > 2800 pounds; 2 tons > 60000 pounces; 1¹/₄tons > 20000 ounces
How to find Inequalities?
1) 5¹/₄ tons when converted to pounds is 10500 pounds.
Thus; 5¹/₄ tons = 10500 pounds.
2) 1/2 ton + 3/4 ton = 5/4 tons
Converting 1.25 to tons gives 2500 tons. Thus;
1/2 ton + 3/4 ton > 2800 pounds
3) Converting 2 tons to Ounces gives 64000 ounces. Thus;
2 tons > 60000 pounces.
4) 1¹/₄tons - ¹/₂ton = ³/₄ tons
Converting to ounces gives 24000 ounces
Thus; 1¹/₄tons > 20000 ounces
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what is the largest 7-digit number and smallest 9-digit number
7-digit:9999999
9-digit: 1000000
Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo.
The dimension of the original photo is 11 inches by 11 inches.
Given that, the area of the reduced photo is 64 square inches.
In the equation [tex](x -3)^{2} = 64[/tex], x represents the side measure of the original photo.
We have to determine the dimensions of the original photo.
What is the equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, solve the equation for the value of x.
By square rooting on both the side, we get
[tex]\sqrt{(x-3)^{2} } =\sqrt{64}[/tex]
⇒[tex](x-3)=[/tex]±[tex]8[/tex]
⇒[tex]x=8+3=11[/tex] and [tex]x=-8+3=-5[/tex]
The length and width can not be negative.
Therefore, the dimension of the original photo is 11 inches by 11 inches.
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Answer: A) 11 inches by 11 inches
Step-by-step explanation:
Edg 2022
Maxwell wants to know how much space his globe occupies. Should he find its surface area or volume? Explain your answer
Since, Maxwell wants to know how much space his globes occupies he has to find its volume.
What is a volume?
Volume is the amount of space an object or substance occupies.
Every three dimensional object occupies a space.
Volume is measured in cubic units.
Therefore, the three dimensional object that has a width, length and height will have its volume as follows;
volume = lwh
where
l = lengthw = widthh = heightTherefore, the space occupied by the globe is the volume of the globe.
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Let D = D(R), where Þ(u, v) = (u², u + v) and
R = [1, 8] × [0, 6].
Calculate
y dA.
Note: It is not necessary to describe D.
Joyda
=
The region [tex]D[/tex] is essentially parameterized in three dimensions by
[tex]\Phi(u,v) = (u^2, u+v, 0)[/tex]
with [tex]1\le u\le8[/tex] and [tex]0\le v\le6[/tex].
The normal vector to [tex]D[/tex] is
[tex]\vec n = \dfrac{\partial\Phi}{\partial u} \times \dfrac{\partial\Phi}{\partial v} = (0,0,2u)[/tex]
with norm [tex]\|\vec n\| = 2u[/tex].
Then the surface integral is
[tex]\displaystyle \iint_D y \, dA = 2 \int_0^6 \int_1^8 (u+v)u \, du \, dv \\\\ = 2 \int_0^6 \left(\frac{1022}3 + 63 v\right) \, dv = \boxed{3178}[/tex]
A magician showed a magic trick where he picked one card from a standard deck. What is the probability that the KING card will be picked?
Answer:
[tex]\frac{1}{13}[/tex]
Step-by-step explanation:
The total number of cards in a standard deck of cards is 52, in which there:
King: 4 cards <----------
Queens: 4 cards
Jack: 4 cards
Ace: 4 cards
Club/Diamond/Heart/Spade: 13 cards
Moreover, 26 of the 52 cards are red, and the remainder 26 are of black.
So the probability that a "king" card will be picked is [tex]\frac{4}{52}[/tex], which can be further simplified [tex]\frac{1}{13}[/tex]
Keiko surveyed people with cell phones. Ages in years = a Texts they send per day = t He drew a best-fit line and determined its equation. Evaluate how many texts a 15 year old would send each day according to Keiko's trend line.
Answer:
68 texts per day
Step-by-step explanation:
The description of the variables in the equation tells you that you want to find t (texts sent per day) for the given value of 'a' (age in years).
__
Substitute the number (15) for the variable (a) and do the arithmetic:
t = -1.63a +92.14
t = -1.63(15) +92.14 = -24.45 +92.14
t = 67.69
Keiko's trend line estimates a 15-year-old would send about 68 texts per day.
Find the volume of the right circular cone with radius 6 cm, height 7 cm
[tex]( \pi = \frac{22}{7} )[/tex]
Answer:
Volume = 264 cm³Step-by-step explanation:
Formula:
Let b be the base (circle) of the cone
and h be the height of the cone
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
……………………………………………
→ b = π × r²
= π × 6²
= (22÷7) × 36
= 113.142857142857 cm²
→ h = 7
[tex]\text{volume of the cone} =\frac{1}{3} \times b\times h[/tex]
The volume = (1÷3)×(113,142857142857)×(7)
= 264 cm³
===================
METHOD 2 :
Volume = (1÷3)×(22÷7)×36×7
= (1÷3)×22×36
= 22×12
= 264
Can someone check this for me please and thank you
Answer:
you're right
Step-by-step explanation:
the answer is false because side AD and sides AE are not the same length, so AB/BD does not equal AC/CE
How do you solve this??
Since diagonals bisect each other, both halves of a diagonal have the same length.
[tex]5y-5=y+23\\4y=28\\y=7\\\\2x-0=x+2\\x=2[/tex]
Therefore b)
Sarah is playing musical chairs. There are twenty people playing and one of them won't be able to find a seat. Find the probability that Sarah will be the person unable to find a seat.
Answer:
Decimal = 0.05
Percentage = 5%
Explanation:
Total count : 20
Sarah count : 1
probability = favorable outcomes/total outcomes
= 1/20
= 0.05
4gal. 2qt - 3gal. 3qt=
I really need help with this please. I would really appreciate it
Answer:
0.75gal.
Step-by-step explanation:
(4gal.) (2qt) - (3gal.) (3qt) =
the easiest way to solve this would be get everything in the same units,
lets make the qt to gallons
2qt = 0.5gal divide the volume value by 4
3qt = 0.75gal
(4gal.) + (0.5gal.) - (3gal.) + (0.75gal.)
= (4.5gal.) - (3.75gal.)
= 0.75gal.
question about college I have straight a’s in all my classes and this year I might be getting a C or lower in one of my classes will that affect my chances into getting accepted into colleges? (average colleges no Ivy League)
The area of the cell phone dimensions to her computer screen dimensions is 1:3. What’s the length and width of the computer screen
Answer:
A=l*w
Step-by-step explanation:
so We Derive Their Formula
L=A/w
An expression is given.
(3x - 1) - 2.75 (x + 2)
Which expression is equivalent to the given expression?
A. 0.25x - 6.50
B. 0.25x + 1.00
C. 0.25x + 4.50
D. 0.25x - 3.00
Find the slope of the line passing through the points (5,8) and (6,12).
Answer:
Calculator soup can help just search for whatever your learning and add a calculator at the end
A bag contained $24.20 worth of coins. There were 20-cent and 50-cent coins only. The number of 20-cent coins was 5 fewer than the number of 50-cent coins. How many coins were there in the bag
Answer:
Their will be 2 coins in allThere were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.
Let x be the number of 50-cent coins in the bag,
And y be the number of 20-cent coins.
From the problem,
we know that y = x - 5,
Since there were 5 fewer 20-cent coins than 50-cent coins.
We can also set up an equation for the total value of the coins in the bag,
⇒ 0.5x + 0.2y = 24.20
Now we can substitute y = x - 5 into the equation,
⇒ 0.5x + 0.2(x - 5) = 24.20
Simplifying, we get,
⇒ 0.7x - 1 = 24.20
⇒ 0.7x = 25.20
⇒ x = 36
So there were 36 50-cent coins in the bag.
Using y = x - 5,
We can find that there were 31 20-cent coins.
Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).
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1. La asistencia a un juego de béisbol profesional fue de 4500 personas y el dinero
recaudado en la entrada fue de CS 49500. Si cada persona compró un boleto de
C$10 o un boleto de C$15 ¿Cuántos boletos de cada tipo se vendieron?
Resolviendo un sistema de ecuaciones veremos que se vendieron 900 boletos de $15 y 3600 boletos de $10.
¿Cuántos boletos de cada tipo se vendieron?
Primero definamos las variables:
x = número de bolteos de $10 vendidos.y = número de bolteos de $15 vendidos.Sabemos que se vendieron 4500 boletos, entonces:
x + y = 4500
Y se recaudo un total de $49,500, entonces:
x*$10 + y*$15 = $49,500
Entonces tenemos un sistema de ecuaciones:
Para resolver esto, primero debemos aislar una de las variables en la primer ecuación, voy a aislar x:
x = 4500 - y
Ahora reemplazamos esto en la otra ecuación:
(4,500 - y)*$10 + y*$15 = $49,500
Ahora debemos resolver estoy para y.
$45,000 - y*$10 + y*$15 = $49,500
y*$5 = $49,500 - $45,000 = $4,500
y = ( $4,500)/$5 = 900
Entonces:
x = 4500 - 900 = 3600
Se vendieron 900 boletos de $15 y 3600 boletos de $10.
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What is the difference between a major arc and a minor arc?
What is the output of this program?
numA = 2
numB = 3
if numA == 2 and numB == 2:
print("yes")
elif numA == 2 and numB == 3:
print("no")
Output:
PLEASE HELP GIVE YOU THE BRAINLEST
Answer:
IUOIUJUIYIYIYUYUYUYIYUYUY
Which equation does the graph of the system of equations solve?
Answer:
d
Step-by-step explanation:
What is the slope-intercept equation for this line? (0,1) ( 1, -2)
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{-2 -1}{1 +0} \implies \cfrac{ -3 }{ 1 }\implies -3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-1=-3x\implies y=-3x+1[/tex]
A family has a monthly income of $3912. Their monthly expenditures are as shown in the graph below.
Rent 21%
Food 24%
Transportation 11%
Other Expenses 18%
Savings 26%
How much money does the family save in a month?
Answer: The save $1134.48
Step-by-step explanation:
3912 x 0.29 = 1134.48
The amount of money that the family saves in a month will be $1,017.12.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
A family has a month-to-month payment of $3912. Their month-to-month uses are displayed in the diagram underneath.
Rent 21%
Food 24%
Transportation 11%
Other Expenses 18%
Savings 26%
Then the amount of money that the family saves in a month is calculated as,
⇒ $3,912 x 0.26
⇒ $1,017.12
The amount of money that the family saves in a month will be $1,017.12.
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Which line on the graph could represent this scenario?
a(x)
f(x)
g(x)
h(x)
Answer: g(x)
Step-by-step explanation:
Question 8: The equation of motion of a particle is
s = t^3 4t^2 + 2t + 8
Where s is in meters
and t is in seconds
Find the acceleration after t=5 seconds.
Answer:
D) [tex]22\:\text{m/s}^2[/tex]
Step-by-step explanation:
Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:
Position of Particle: [tex]s(t)=t^3-4t^2+2t+8[/tex]
Velocity of Particle: [tex]v(t)=3t^2-8t+2[/tex]
Acceleration of Particle: [tex]a(t)=6t-8[/tex]
After [tex]t=5[/tex] seconds, the acceleration of the particle is [tex]a(5)=6(5)-8=30-8=22\:\text{m/s}^2[/tex]
The acceleration of the particle after 5 seconds is 38 m/s².
What is acceleration?Acceleration is the rate of change of velocity or the slope of velocity.
We know that the first derivative of motion or speed is velocity and the second derivative of motion or speed is acceleration.
∴ We have to take the derivative of s = t³ + 4t² + 2t + 8 twice to obtain the equation of acceleration and replace t with 5 to get the acceleration value after 5 seconds.
Now, s = t³ + 4t² + 2t + 8 meters.
ds/dt = 3t² + 8t + 2 m/s.
d²s/dt² = 6t + 8m/s²
Now, at t = 5 seconds d²s/dt² = 6t + 8 is,
d²s/dt² = 6(5) + 8 m/s².
d²s/dt² = 38 m/s².
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what equation is equivalent to 2^3^x =10
Answer:
[tex]log_2(10)[/tex]
how to findSimplify the equation using logarithms.
part 1[tex]2^3x=10[/tex]
[tex]log_1_0(2^3x)=log_1_0(10)[/tex]
log rule ⇩
[tex]log_a(x^y)=y*log_a(x)[/tex]
move exponent out of log.
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
part 2isolate variable further
[tex]x*log_1_0(2)=log_1_0(10)[/tex]
[tex]x=\frac{log_{10}(10)}{log_{10}(2)}[/tex]
formula for combining logs. ⇩
[tex]\frac {log_b(x)}{log_b(a)}=log_a(x)[/tex]
the result ⇩
[tex]x=log_2(10)[/tex]