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
Which function is represented in this graph?
Step-by-step explanation:
we can see that this is an absolute value function. we know that for the graph to be shifted to the left the value of the constant inside the absolute value should be positive. and the fact that it is shifted down means that there is a negative constant outside the absolute value. the equation is:
| X + 5 | - 1
The linear equation y = 35x describes how far from home Deena is as she drives from San Francisco to Dawson. Let x represent the number of hours and y represent the number of miles. How far from home is Deena in 12 hours? Graph the equation and tell whether it is linear.
Deena is 420 miles from home in 12 hours.
The graph is shown below. The graph is linear
Solving linear equationsFrom the question, we are to determine how far Deena is from home in 12 hours
From the given linear equation,
y = 35x
We are to determine how far Deena is from home in 12 hours
That is,
x = 12 hours
Put x = 12 into the equation,
∴y = 35(12)
y = 420 miles
Hence, Deena is 420 miles from home in 12 hours.
The graph is shown below. The graph is linear
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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
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
What is the difference between a major arc and a minor arc?
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
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.
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]
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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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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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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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 line on the graph could represent this scenario?
a(x)
f(x)
g(x)
h(x)
Answer: g(x)
Step-by-step explanation:
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
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.
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
Вхід на станцію метрополітену обладнаний системою к=4 турнікетів. При виході з ладу одного з турнікетів решта продовжують нормально функціонувати. Вхід на станцію перекривається, якщо вийдуть з ладу всі турнікети. Потік відмовлень кожного турнікету - найпростіший, середній час безвідмовної роботи одного турнікету 175 годин. При виході з ладу кожний турнікет починає відразу ремонтуватися. Час ремонту розподілено за показниковим законом і в середньому складає 5-3 годин. В початковий момент всі турнікети справні. Знайти середню пропускну спроможність системи турнікетів у відсотках від номінальної, якщо з виходом з ладу кожного турнікету система втрачає (100/k) % своєї номінальної пропускної спроможності
Write an expression to describe the
situation.
A car travels 50 miles per hour, h. What expression
represents the total distance you've traveled?
Answer:
m = 50h, where m is the distance traveled in miles
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]
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!
Which equation does the graph of the system of equations solve?
Answer:
d
Step-by-step explanation:
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)
The tables show the cost (in dollars) of colored pencils at two stores. Brendan says that the school store offers a better deal than the corner store. Which statement is correct? A. Brendan is right. B. Brendan is wrong because both stores offer the same deal. C. Brendan is wrong because you cannot compare the offers. D. Brendan is wrong because the corner store offers a better deal than the school store.
Answer:
B
Step-by-step explanation:
I got it right on the test
Answer:
B
Step-by-step explanation:
Express GHD80.00 as a percentage of GHD320.00
Answer:
If using a calculator, you can calculate one number as a percentage of another by dividing the numbers and multiplying by 100.
Step-by-step explanation:
what is the largest 7-digit number and smallest 9-digit number
7-digit:9999999
9-digit: 1000000
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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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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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]