the answer is 1 5/8 inches shorter. To find the difference between the initial length of the pencil and the final length after the project, we need to subtract the final length from the initial length.
Initial length of the pencil = 7 1/2 inches
Final length of the pencil = 5 7/8 inches
To subtract these two values, we need to convert the mixed numbers to improper fractions.
7 1/2 = 15/2
5 7/8 = 47/8
Now we can subtract:
15/2 - 47/8
To subtract these fractions, we need to find a common denominator. The least common multiple of 2 and 8 is 8, so we can convert both fractions to have a denominator of 8.
15/2 = 60/8
47/8 = 47/8
Now we can subtract:
60/8 - 47/8 = 13/8
So the pencil is 13/8 inches shorter after the project. To write this as a mixed number, we divide the numerator by the denominator:
13 ÷ 8 = 1 with a remainder of 5
So the answer is 1 5/8 inches shorter.
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what is the domain of the function?
Answer:
(-infinity, -11) U (-11, 9) U (9, infinity)
Step-by-step explanation:
we have to restrict this so that the denominator isn't 0
to find this, we can factor the denominator to (x+11)(x-9). the zeroes, then, are x=-11 and x=9.
so, the domain must exclude these values, and we get (-infinity, -11) U (-11, 9) U (9, infinity)
suppose that a voting facility processes an average of 55 people per hour (throughput) and that, on average, it takes 30 minutes for each person to complete the voting process (flow time).
The required average number of people completing voting at any given time as per given 55 people per hour is equals to 27.5.
Average throughput voting facility process = 55 people per hour,
Calculate the average processing time per person ,
⇒ Processing time per person = 1 hour / 55 people
⇒ Processing time per person = 0.01818 hours/person
Average time taken by each person to complete the voting process = 30 minutes
Convert this to hours by dividing by 60,
⇒ Flow time per person = 30 minutes / 60
⇒ Flow time per person = 0.5 hours/person
Now,
Average number of people in the voting facility using Little's Law,
which states that the average number of items in a system is equal to the average throughput multiplied by the average flow time.
⇒ Average number of people in facility = Average throughput x Average flow time
⇒ Average number of people in facility = 55 people/hour x 0.5 hours/person
⇒ Average number of people in facility = 27.5 people
Therefore, on average there are 27.5 people in the voting facility at any given time.
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The above question is incomplete, the complete question is:
Suppose that a voting facility processes an average of 55 people per hour (throughput) and that, on average, it takes 30 minutes for each person to complete the voting process (flow time).Calculate the average number of people in the voting facility at any given time.
A piece of property contains 1,758.1066 sq. yards. How many yards are on each side of the square?
Answer: approximately 41.96 yards
Step-by-step explanation:
If a square property contains 1,758.1066 square yards, then the area of the square is equal to this value.
Let x be the length of each side of the square. Then, the area of the square can be expressed as x^2.
So we have:
x^2 = 1,758.1066 sq. yards
Taking the square root of both sides gives:
x = √1,758.1066
x ≈ 41.96 yards
Therefore, each side of the square is approximately 41.96 yards long.
Each side of the square is approximately 41.9143 yards long.
For the function p = 2 - 3q². what is the instantaneous rate of change function?
Answer:
Step-by-step explanation:
To find the instantaneous rate of change function for the given function p = 2 - 3q², we need to find the derivative of the function with respect to q. The derivative gives us the slope of the tangent line to the curve at any point, which is the instantaneous rate of change at that point.
So, we can start by taking the derivative of the given function:
dp/dq = d/dq(2 - 3q²)
dp/dq = 0 - 3(2q)
dp/dq = -6q
Therefore, the instantaneous rate of change function for p = 2 - 3q² is given by:
dp/dq = -6q
This means that the instantaneous rate of change (slope of the tangent line) of the function p with respect to q is -6q at any given point.
Which graph represents the solution to inequality
Graph c is the correct solution of the given inequality.
EquationsTo solve the inequality 11 <= y - 43, we need to isolate y on one side of the inequality.
Adding 43 to both sides, we get:
11 + 43 <= y - 43 + 43
54 <= y.
How to represent inequality on a number line?Draw a number line and mark any relevant points. For example, if the inequality involves x > 3, mark the point 3 on the number line.
Determine if the inequality is "greater than" (>), "less than" (<), "greater than or equal to" (≥), or "less than or equal to" (≤).
For a "greater than" or "greater than or equal to" inequality, shade the line to the right of the relevant point(s) on the number line. For a "less than" or "less than or equal to" inequality, shade the line to the left of the relevant point(s) on the number line.
If the inequality includes "and," place another shade for the second part of the inequality. The solution is where the two shaded regions overlap.
If the inequality includes "or," draw two separate number lines for each part of the inequality and shade the appropriate regions. The solution is the combination of the two separate shaded regions.
Indicate whether the endpoints are included or excluded, using an open circle for excluded endpoints and a closed circle for included endpoints.
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Ashley invested $59,000 in an account paying an interest rate of 3 1/8% compounded daily. Fwam invested $59,000 in an account paying an interest rate of 2 3/4% compounded annually. . After 15 years, how much more money would Ashley have in her account than Fwam, to the nearest dollar?
The difference between the balances of Ashley and Fwam after 15 years is given as follows:
$5,650. (Ashley will have $5,650 more than Fwam).
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.Hence Ashley's amount after 15 years is given as follows:
A(15) = 59000 x (1 + 0.03125/365)^(365 x 15)
A(15) = $94,280.
Fwam's amount is given as follows:
F(15) = 59000 x (1 + 0.0275)^(15)
F(15) = $88,630.
Then the difference is of:
94280 - 88630 = $5,650.
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Answer:5650
Step-by-step explanation:
94279.8393-88629.7389=5650.1009
Challenge Question: 146.794/0.643 I bet u 100 bucks to do it!!!!!!
The answer would be 228.295489891
Rounded to the nearest tenth it would 228.3
Please help me with this function problem！
The derivative of the function is (5/2)x² - 2, the critical points are [tex](\frac{2\sqrt{5} }{5}, -\frac{8\sqrt{5} }{15}), (-\frac{2\sqrt{5} }{5}, \frac{8\sqrt{5} }{15})[/tex], the points of inflection of the function is at (0,0)
What is the value of f'(x)(a) The derivative of f(x) is f'(x) = (5/2)x² - 2.
(b) The critical points occur where f'(x) = 0 or where f'(x) is undefined.
Setting f'(x) = 0, we get (5/2)x² - 2 = 0,
[tex](\frac{2\sqrt{5} }{5}, -\frac{8\sqrt{5} }{15}), (-\frac{2\sqrt{5} }{5}, \frac{8\sqrt{5} }{15}[/tex]
(c) f'(x) = (5/2)x² - 2 is positive when x > (2√5)/5 and negative when x < (-2√5)/5. Therefore, f(x) is increasing on the interval
[tex](-\infty, -\frac{2\sqrt{5} }{5}), (\frac{2\sqrt{5} }{5}, \infty)\\[/tex] and it decreases along the interval of
[tex](-\frac{2\sqrt{5} }{5}, \frac{2\sqrt{5} }{5})[/tex]
(d) The second derivative of f(x) is f''(x) = 5x
(e) f''(x) is positive when x > 0 and negative when x < 0. Therefore, f(x) is concave up on the interval (0, infinity) and concave down on the interval (-infinity, 0).
(f) The points of inflection for f(x) are (0,0)
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Need the area of the parallelogram
Answer:
Step-by-step explanation:
4 * 7= 28
Answer:
28
Step-by-step explanation:
hope i help u:)
Waffle Wonderland puts a 250-milliliter bottle of maple syrup on each one of their 16 tables. The owner is filling the syrup bottles before the restaurant opens. If the bottles are half full, how many liters would she need to fill the bottles?
PLEASE HELP ME MATH. I WILL GIVE BRAINLISEST
the value οf f(h(-1)) will be ∛2.
What is a functiοn?A unique kind οf relatiοn called a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn prοduces exactly οne value fοr each input value. The graphic abοve shοws a relatiοn rather than a functiοn because οne is mapped tο twο different values. The relatiοn abοve wοuld turn intο a functiοn, thοugh, if οne were instead mapped tο a single value. Additiοnally, οutput values can be equal tο input values.
The x-values are input intο the functiοn machine. The functiοn machine then perfοrms its οperatiοns and οutputs the y-values. The functiοn within can be any functiοn.
f(x) = ∛x+3
g(x)= 8x³-3
h(x)= 2x+1
f((h(-1))= f(-1) = ∛2
Hence the value οf f(h(-1)) will be ∛2.
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Wolf packs in the Northern Yukon Territory have territories of various sizes. Pack A has a territory of 900km^2 and of that 600km^2 are mountainous. Pack B has a territory of 700km^2 with 500km^2 being mountainous. Do both territories have the same ratio of mountains to the total range? Write each ratio in the simplest form and compare.
The ratio of pack A is 3 : 2 [tex]km^{2}[/tex] and for pack B is 7 : 5 [tex]km^{2}[/tex] . Pack A has more of mountainous territory.
What is ratio?
One can calculate how much of one quantity is included in the other by comparing two amounts of the same unit and obtaining the ratio.
We are given two packs.
Pack A has a territory of 900 [tex]km^{2}[/tex] and of that 600 [tex]km^{2}[/tex] are mountainous.
So, the ratio in the simplest form is 3 : 2 [tex]km^{2}[/tex] .
Similarly, Pack B has a territory of 700 [tex]km^{2}[/tex] with 500 [tex]km^{2}[/tex] being mountainous.
So, the ratio in the simplest form is 7 : 5 [tex]km^{2}[/tex] .
On comparing the ratios, we get that Pack A has more of mountainous territory than Pack B.
Hence, both territories do not have the same ratio of mountains to the total range.
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whats 1/2 divided by 17 pls help me with this
Answer: 0.0294117647
Find the length of the missing side of the trapezoid below. [asy] size( 100 ) ; real top = 5 ; real bottom = 8 ; real height = sqrt(40) ; real slant = 7 ; pair ll = (-bottom,0) ; pair lr = (0,0) ; pair ur = lr+(0,height) ; pair ul = ur-(top,0) ; draw( ll--lr--ur--ul--cycle ) ; draw(rightanglemark( ur , lr , ll , 20 )) ; draw(rightanglemark( ul , ur , lr , 20 )) ; label( "$"+string(bottom)+"$" , ll--lr , S ) ; label( "$"+string(top)+"$" , ul--ur , N ) ; label( "$"+string(slant)+"$" , ul--ll , W ) ; [/asy] Give your answer in simplified form.
As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.
what is pythagoras theorem ?A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to Pythagoras' Theorem, is equal to the sum of the squares of the lengths of the other two sides (the legs). Formally, Pythagoras' theorem asserts that if a right triangle has legs of lengths a, b, and c, and a hypotenuse of length c, then:
[tex]a^2 + b^2 = c^2[/tex]
Pythagoras, an ancient Greek mathematician, is credited with discovering and proving this theorem, therefore it bears his name.
given
The Pythagorean theorem can be used to determine the length of the omitted side. Let x be the length of the side that is missing. The right triangle that results has a hypotenuse that is top-bottom in length and legs that are x and slant in length. This can be expressed as:
x2 + slant2 = (top - bottom)2
$$
To put it simply, we have:
\begin{align*} \s(top - bottom) (top - bottom)
2 &= x 2 + slant 2, top 2 - 2top "cdot bottom + bottom 2 - slant 2," x 2 &= "sqrt" top 2 - 2top "cdot bottom + bottom 2 - slant 2," and "end align"
begin-aligning* x = sqrt((5),2,5,8,and(8),2,-7,2). sqrt = 25 - 80 + 64 - 49; sqrt = 40; sqrt = boxed 2i sqrt 10; end align;
As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.
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Express answer in exact form. Show all work for full credit.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3 .)
The area of the segment formed by a side of the hexagon and the circle is (3π - 9 √(3)) / 4 square inches.
How to calculate area of segment formed?A regular hexagon ABCDEF inscribed in a circle with center O. Let's consider the segment bounded by side AB and the arc ACB. We want to find the area of this segment.
First, find the central angle of the sector AOC. Since the hexagon is regular, the central angle of each sector is 60 degrees. Therefore, the central angle of AOC is 120 degrees.
Next, find the area of sector AOC by using the formula for the area of a sector:
Area of sector AOC = (central angle / 360) × π × radius²
= (120 / 360) × π × (3 / 2)²
= (1 / 3) × π × 9 / 4
= (3 / 4) × π
Now, find the area of triangle AOB. Since the hexagon is regular, triangle AOB is equilateral with side length 3". Therefore, use the formula for the area of an equilateral triangle:
Area of triangle AOB = (1 / 4) × (3)² × √(3)
= (9 / 4) × √(3)
Finally, find the area of the segment by subtracting the area of triangle AOB from the area of sector AOC:
Area of segment AB = Area of sector AOC - Area of triangle AOB
= (3 / 4) × π - (9 / 4) × √(3)
= (3 π - 9 √(3)) / 4
Therefore, the area of the segment formed by side AB and the circle is (3 π - 9 × √(3)) / 4 square inches.
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I need help with this please
Answer: 2 7/8 = 23/8
Step-by-step explanation:
1/8+1/8 = 2/8 = 1/4 (add w/ other 3) (This is not added to the final equation since added at the one below this)
1/4+1/4+1/4+1/4=1
3/8+3/8+3/8= 9/8 = 1 1/8
3/4 = 6/8
Add them
1 + 1 1/8 + 6/8 = 2 7/8
HELPPPPPPPPPPPP Plsss
Answer:
x ≈ 13,6; y ≈ 15,7; z ≈ 26,7
Step-by-step explanation:
I added a photo of my solution
Answer: Answer is below <3
Step-by-step explanation:
x - 13,6y - 15,7z - 26,7Last year 525,398 people walked across the Golden Gate Bridge. This year 650,482 people walked across the Golden Gate Bridge. How many more people walked across the Bridge this year as compared to last year?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Question reads..}[/tex]
[tex]\textsf{Last year 525,398 people walked across the Golden Gate Bridge. This year 650,482}\\\textsf{people walked across the Golden Gate Bridge. How many more people walked}\\\textsf{across the Bridge this year as compared to last year?}[/tex]
[tex]\huge\text{Well when we come across..}[/tex]
[tex]> \textsf{When are comparing two (or more numbers), we are either SUBTRACTING or}\\\textsf{ADDING the numbers, it all depends on how you read the word problem. That is}\\\textsf{we have to read the word problem CAREFULLY so we can know what operation }\\\mathsf{(+,-, \div, \times)}\textsf{ we are doing}[/tex]
[tex]\huge\text{If that is the case, we are doing in this}\\\\\huge\text{word problem..}[/tex]
[tex]> \textsf{We are SUBTRACTING because we are COMPARING \underline{CURRENT year}}\\\textsf{with the \underline{PAST year}}}[/tex]
[tex]\huge\text{What should the equation look like right off the}\\\\\huge\text{top of your head?}[/tex]
[tex]\mathsf{650,482 - 525,398}[/tex]
[tex]\huge\text{Just SOLVE it like a regular basic arithmetic}\\\huge\text{equation}[/tex]
[tex]\mathtt{650,482 - 525,398}[/tex]
[tex]\text{Start with the bigger number (650,482) \& go down however many spaces you} \\\text{have for the smaller number (525,398).}[/tex]
[tex]\rightarrow\mathtt{125,084}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathtt{125,084}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
125,084 more people walked across the Bridge this year, compared to last year.
Step-by-step explanation:
To find how many morepeople walked across the bridge in the current year compared to last year, woth the number of this year being larger than last year's, simply subtract the larger number from the smaller number by hand or using a calculator:
650,482 - 525,398= 125,084.
Therefore, 125,084 more people walked across the Bridge this year, compared to last year.
In case you need to do this subtraction by hand, check the attached image to see the process.
write absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that has the following solution set: x is less than or equal to 5
The absolute value equations in the form of |x-b|= c(where b is a number and c can be either a number or an expression) that has the following solution set
all numbers such that x ≤ 5 and all numbers such that x ≥ -1.3 will be x -5 ≤ 0 and x + 1.3 ≥ 0.
Isolate the absolute number on one side of the equation to solve an equation containing the absolute value.
Then, resolve both equations by changing their respective contents to the positive and negative values of the variable on the other side of the equation.
In another word, the absolute value equation is the equation that has a real absolute value not imaginary and not binary.
In the mode function, it could be two values if the mode is going negative or positive.
Given that the equation |x-b| = c and the constraint is
all numbers such that x ≤ 5
all numbers such that x ≥ -1.3
so by substituting we will get x -5 ≤ 0 and x + 1.3 ≥ 0.
The complete question is-
Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that has the following solution set
all numbers such that x ≤ 5
all numbers such that x ≥ -1.3
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PLEASE HELP WILL MARK BRAINLIEST!
A portion of the quadratic formula proof is shown. Fill in the missing statement.
Answer: THE ANSWER IS 3 BECAUSE I HAD THIS TEST
RATE BRAINLIEST PLEASE
Step-by-step explanation:
Answer question no.3
The diagonal of the Rhombus intersect at point M and thus, m<IMJ is 90 degrees
How to prove the angleIt is important to note the properties of a Rhombus, they are;
All sides of the rhombus are equal.Opposite sides of a rhombus are parallel.Opposite angles of a rhombus are equal.Diagonals bisect each other at right angles, that is 90 degrees in a Rhombus.Diagonals bisect the angles of a rhombus.The sum of two adjacent angles is equal to 180 degrees.From the diagram shown, we can see that the diagonals are;
Diagonal 1: JL
Diagonal 2: IK
These diagonals intersect at point M and since diagonals in a Rhombus intersect at right angles, that is , 90 degrees.
Then, m< IMJ is 90 degrees
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YOU START A BAnK aCCOUnt With $500, ANd THE intEREST ON thE ACCOUnT iS 8% every year. How MUCH IS IN THE ACCOUNT AFTER 19 YEARS?
We can conclude after answering the provided question that Therefore, interest after 19 years, the amount in the account will be $1,418.50.
what is interest ?In mathematics, interest is the sum of money earned but rather owed on an initial investment or loan. You can use either simple or compound interest. Rate of return is computed upon that main fee plus any previously earned interest, whilst simple interest is given as a percent of the initial amt. If you invest $100 at a 5% each year simple interest rate, you will earn $5 through interest every year for four years, for a total of $15.
calculating the future value of an investment is:
[tex]FV = PV x (1 + r)^n\\FV = $500 x (1 + 0.08)^19\\FV = $500 x 2.837\\FV = $1,418.50[/tex]
Therefore, after 19 years, the amount in the account will be $1,418.50.
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Can you solve this quesiton?
f'(x)=?
f'(4)=?
On diffrentiating 1.f'(x)=8xsinx + 4x²cosx
Putting the value variable x=4, 2. f'(4)=66.07
What Is Mathematical Differentiation?Differentiation in mathematics is a function's derivative with respect to an independent variable. Calculus's concept of differentiation may be used to calculate the function per unit change in the independent variable.
Y = f would be a function of x. (x)
Secondly, the following is the formula for the rate of change of "y" per unit change in "x":
dy / dx
Given function:
f(x)=4x²tanx/secx
f(x)=(4x²sinx/cosx)× cosx
f(x)=4x²sinx
On differentiating f(x), we get
f’(x)=8xsinx+4x²cosx
Putting the values at x=4, we get
f’(4)=8×4×sin4+4(4)²cos4
f’(4)=66.07
Hence, f’(x)=8xsinx + 4x²cosx
f’(4)=66.07
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PLEASE HELP WITH THESE TWO QUESTION 20 POINTSSSS
In the given question angle a= 60° and b= 120° by exterior angle theorem
How are exterior angles determined?When a triangle's side is extended to make an angle outside the triangle, the external angles of the triangle are formed. We can use the formula below to determine the size of an external angle:
Sum of Measurements of Distant Interior Angles = Measure of Exterior Angle
The two interior angles that are not directly close to the external angle being measured are known as the remote interior angles. Remote internal angles are angles at vertices A and B if we extend the side AB to generate an exterior angle at vertex C in a triangle with vertices A, B, and C.
Measure of Interior Angle at Vertex A + Measure of Interior Angle at Vertex B = 180 degrees, where Measure of Exterior Angle at Vertex C = 180 degrees.
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i needed help finding x y and z
The value of the given relation of the parallelogram to justified the relation of the given part is x = 7, y = 9 and z = 17.
What about the property of parallelogram?
A parallelogram is a four-sided flat shape that has two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are also equal. The parallel sides of a parallelogram are usually denoted by "a" and "b", while the height or perpendicular distance between the parallel sides is denoted by "h"
Define relation:
A relation is a set of ordered pairs that describe the relationship between two or more variables. Specifically, a relation is a set of ordered pairs (x, y) where x and y belong to some sets of objects, called the domain and range, respectively.
For example, consider the relation R between the set of all real numbers and itself defined by:
R = {(x, y) | y = x²}
This relation is a set of ordered pairs where the second element (y) is equal to the square of the first element (x). In this case, the domain and range of the relation R are both the set of all real numbers.
According to the given information:
As, we know opposite side of parallelogram are equal so,
10x + 14 = x + 77
9x = 63
x = 7
In the same way we also know that in case of parallelogram diagonal bisect equally to each other so,
4y-19 = y + 8
3y = 8 + 19
y = 9
And,
2z + 3 = 37
2z = 34
z = 17
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Carson bought a cost for 40% of the original price, then another 15% off the discounted price. If the cost originally coast $149, what was the final sale sale price Carson paid.
The final price Carson paid was $75.99.
The original cost of the item is $149.
Carson bought the item for 40% off the original price, which means he paid:
$149 x 0.6 = $89.40
Carson paid only $89.40 after he got a 40% discount.
Now, Carson receives an additional discount of 15% off the discounted price. This means he pays:
$89.40 x 0.85 = $75.99
After getting an additional discount of 15% Carson paid $75.99 only.
Therefore, Carson's final sale price for the item was $75.99 after getting 40% and additional 15% discount.
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Find the unit rate in feet per second
120yards
3 minutes
Answer:
120 ft / sec
Step-by-step explanation:
to know how many yards in 1 sec
120 yd ÷3 = 40 yd
so 40 yd/sec
to make them in feet per sec
1 yd= 3 ft
40 yd ×3 ft = 120 ft
so, 120 ft/sec
Which expression is equivalent to the given expression? - 2 x 2 + 8 x − 9 + 4 x + 7 x 2 + 2 A. - 9 x 2 − 12 x + 11 B. - 5 x 2 + 4 x + 11 C. 5 x 2 + 12 x − 7 D. - 9 x 2 + 4 x − 7
Answer: Option C = 5x^2 + 12x - 7
Step-by-step explanation: First, we need to combine like terms.
-2x^2 + 8x - 9 + 4x + 7x^2 + 2 = (7x^2 - 2x^2) + (4x + 8x) + (-9 + 2) = 5x^2 + 12x - 7
So the expression is equivalent to option C, which is 5x^2 + 12x - 7.
Answer:
ITS THE FIRST ONE
Step-by-step explanation:
-2X2+8
HOPE THIS HELPS
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40
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Mark this and return
7 8
Which statement describes what these four powers have in common?
10
(-2)⁰
– ادب
O All the powers have a value of 0 because the exponent is zero.
O All the powers have a value of 1 because the exponent is zero.
O All the powers have a value of -1 because the exponent is zero.
O All the powers have a fractional value because the exponent is zero.
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The option 2 is correct of given question ''All the powers have a value of 1 because the exponent is zero.''
What do you mean by Exponent?An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript number to the right of the quantity being multiplied.
For example, in the expression 5³, 5 is the base and 3 is the exponent. This means that 5 is being multiplied by itself three times: 5 x 5 x 5, which equals 125.
The statement "All the powers have a value of 1 because the exponent is zero" describes what these four powers have in common.
When the exponent is zero, any number (except for 0) raised to the power of 0 equals 1. Therefore, 10⁰ = 1, (-2)⁰ = 1, and any non-zero number raised to the power of 0 equals 1.
There is no fractional value involved in this case, as raising a number to the power of zero does not involve any division.
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Complete question:
Please Help Solve This Geometry Problem
So ΔOAP≅ΔOBQ(by AAS) so OA ≅ OB(CPCTC) and PO ≅ OQ(CPCTC)
What do you mean by AAS Theorem ?The AAS theorem, also known as the angle-angle-side theorem, is a theorem in Euclidean geometry that states: "If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent."
Given that,
AP ≅ BQ
AP ⊥ AB and BQ ⊥ AB
so ∠A = 90° and ∠B = 90°
To prove that
AO ≅ BO and PO ≅ OQ
In ΔOAP AND ΔOBQ
AB ≅ BQ (given)
∠A = ∠B = 90°
∠AOP = ∠BOQ (vertically opposite angle theorem)
Therefore,Δ OAP ≅ Δ OBQ
∴ OA ≅ OB (CPCT)
PO ≅ OQ (CPCT)
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