Answer:
32[tex]m^{2}/min[/tex]
Step-by-step explanation:
We let the length of the square be l, the diagonal be z and the area be A.
Then by Pythagoras theorem;
[tex]l^{2}+l^{2}=z^{2}\\2l^{2}=z^{2}[/tex]
The are of a square of length l is given as;
[tex]A=l^{2}[/tex]
Combining these two equations yields;
[tex]z^{2}=2A[/tex]
[tex]A=\frac{z^{2} }{2}[/tex]
Next, we have been given;
[tex]\frac{dz}{dt}=8[/tex]
We are required to find;
[tex]\frac{dA}{dt}[/tex] when z = 4
By chain rule;
[tex]\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt}[/tex]
Differentiating [tex]A=\frac{z^{2} }{2}[/tex] with respect to z yields;
[tex]\frac{dA}{dz}=z[/tex]
Therefore,
[tex]\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt}[/tex] = 8z
When z is 4m the area of the square will be increasing at a rate of;
8m/min * 4m = 32[tex]m^{2}/min[/tex]
The area of the square is increasing at a rate of 32 m^2/min when the diagonals are each 4 meters long. This is calculated using the relationship between the diagonal and the side length of the square, and applying the concepts of calculus.
Explanation:The subject of your question is related to Mathematics, specifically in the field of calculus, which deals with rates of change and accumulation. In this scenario, we're looking at how fast the area of a square is increasing given that its diagonals are increasing at a steady rate.
In a square, the diagonal and the side length 's' have a specific relationship, given by the Pythagorean theorem as diagonal = s * sqrt(2). As the diagonal is increasing at 8 m/min, ds/dt = 8/(sqrt(2)) m/min. Now, the area of a square (A) is given by A = s^2. By differentiating this respect to time 't', dA/dt = 2s*(ds/dt). Substituting the given length of the diagonal (4 m), we find s = diagonal/sqrt(2) = 2 sqrt(2) m. Now, substituting s and ds/dt into the equation for dA/dt, we find dA/dt = 2s*(ds/dt) = 2*2sqrt(2)*8/sqrt(2) = 32 m^2/min. So, the area of the square is increasing at the rate of 32 m^2/min when the diagonals are 4 meters each.
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Which of the following is a statistical question?
What color are Mr. Bryant's eyes?
How many pencils are in each person's desk?
How many days are in June? Do you like bananas?
Answer:
How many pencils are in each person's desk?
Which expression is equivalent to 3.5x + 4.8?
(A.) 3 • 0.5x + 4 • 0.8
(B.) 3x • 0.5x + 4 • 0.8
(C.) 3 + 0.5x + 4 + 0.8
(D.) 3x + 0.5x + 4 + 0.8
Answer:
i think its c
Step-by-step explanation:
cus u can multiply 3x or 3
Answer: 68.34.56
Step-by-step explanation:
What are the solutions of x^2-2x+26=0?
Answer:
x = 1 + (i)5 and x = 1 - (i)5
Step-by-step explanation:
x^2-2x+26=0 can be rewritten by completing the square of x^2-2x, as follows:
x^2-2x+26=0
x^2-2x+ 1 - 1 +26=0 (this 1 comes from halving the coefficient of x (which is -2), obtaining -1, squaring the result, and then adding this 1 to and subtracting this 1 from x^2-2x) → x^2-2x+ 1 - 1 +26=0
Rewriting x^2-2x+ 1 as the square of a binomial, we get:
(x - 1)² - 1 +26=0, or (x - 1)² - 1 +26=0, or (x - 1)² = -25
Taking the square root of both sides yields x - 1 = ±(i)5.
Thus, the roots are x = 1 + (i)5 and x = 1 - (i)5 (Answer C)
the product of 2 rational numbers is 16/19. if one number is -4/3, find the other
Answer:
24/ -38
Step-by-step explanation:
We have to do the opposite of multiplication here, which is division.
If the product is 16/19 and a factor is -4/3 then : (16/19) / (-4/3)
Lets flip the switch, meaning change the symbol and flip the fraction: (16/19) * (3/-4)
Multiply 16 * 3 = 48
19 * -4= -76
We now have the fraction 48/-76
When simplified it will be: 24/-38
Jim spends 30 minutes writing 10 sentences (slowpoke!). If he has 30 more sentences to write and continues writing at this same rate, how long should it take him to finish the entire assignment? (I know the answer it's just that I want to see if anyone is going to reply...probably not)
Answer:
90 minutes
Step-by-step explanation:
If Jim takes 30 minutes to write 10 sentences, we can write a proportion.
[tex]\frac{30}{10}=\frac{x}{30}[/tex]
Cross multiply so we get [tex]10x=900[/tex].
And simplify.
[tex]x=90[/tex]
Ratio of a to c
Please answer
Answer:
Step-by-step explanation:
a/b=4/5 b/c=2/9
Ration of a to c is
a/c=4/9
Answer:
[tex]\frac{8}{45}[/tex]
Step-by-step explanation:
[tex]\frac{a}{c}[/tex] = [tex]\frac{a}{b}[/tex] × [tex]\frac{b}{c}[/tex]
= [tex]\frac{4}{5}[/tex] × [tex]\frac{2}{9}[/tex] = [tex]\frac{8}{45}[/tex]
What’s the answer to this please ?
Answer:
YesStep-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
ΔABC:
A(2, 5), B(5, 5), C(5, 9)
[tex]AB=\sqrt{(5-2)^2+(5-5)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\AC=\sqrt{(5-2)^2+(9-5)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\BC=\sqrt{(5-5)^2+(9-5)^2}=\sqrt{0^2+4^2}=\sqrt{0+16}=\sqrt{16}=4[/tex]
ΔDEF:
D(-7, 8), E(-4, 8), F(-4, 4)
[tex]DE=\sqrt{-4-(-7))^2+(8-8)^2}=\sqrt{3^2+0^2}=\sqrt{9+0}=\sqrt9=3\\\\DF=\sqrt{(-4-(-7))^2+(4-8)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\EF=\sqrt{(-4-(-4))^2+(4-8)^2}=\sqrt{0^2+(-4)^2}=\sqrt0+16}=\sqrt{16}=4[/tex]
AB ≅ DE
AC ≅ DF
BC ≅ EF
Therefore ΔABC ≅ ΔDEF
plz help me brainliest to whoever answers first.
Answer:
Second is the answer
Step-by-step explanation:
Slope = rise/run = y /x = m
Solve y to get y = mx
The slope of a line is rise over run, which would be Y over X.
The second answer is the correct one.
What is the average number of voters per precinct ?
Answer:
197
Step-by-step explanation:
Add the number of voters of each precinct and divide by the number of precincts.
(168 + 240 + 195 + 180 + 312 + 87)/6 =
= 1182/6
= 197
(168+240+195+180+312+87)/6 =197
Centerville Middle School spends $11 for every workbook it buys. At most how many workbooks can Centerville Middle School buy if it has $22 to spend?
If you divide 22 by 11 you get two.
Your answer is 2.
Since 1 book cost $11, you divide $22 by 11 which would give you 2. So they can only purchase 2 books.
What is the solution for the following system of equations? x +2y=6
Answer: Infinitely many solutions
Step-by-step explanation:
Write all the facts for the fact family 3,8,24
3 x 8 = 24
8 x 3 = 24
24/3 = 8
24/8 = 3
A prime number is a number that has a factor of 1 and the number itself.
A factor is a number that we use to get the multiples of a number.
The facts for the fact family 3, 8, and 24 are:
3 and 8 multiplied can give 24.
8 and 24 is a multiple of prime numbers 2 and 3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
3, 8, and 24.
We see that,
3 and 8 multiplied can give 24.
3 x 8 = 24
8 and 24 is a multiple of prime numbers 2 and 3.
Prime numbers are those numbers that have a factor of 1 and the number itself.
2 x 4 = 8
2 x 12 = 24
3 x 8 = 24
2 and 3 are prime numbers.
Thus,
The facts for the fact family 3, 8, and 24 are:
3 and 8 multiplied can give 24.
8 and 24 is a multiple of prime numbers 2 and 3.
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What is the measure of
A) 44
B)131
C)175
D)49
E)93
F)87
Answer: 175
Step-by-step explanation: I hope this helps!!
Answer:
D
Step-by-step explanation:
ACD is a straight angle, thus
∠ACB + ∠BCD = 180. thus
∠ACB 131 = 180 ( subtract 131 from both sides )
∠ACB = 49° → D
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.
Answer:
h = 10sin(π15t)+35
Step-by-step explanation:
The height of the blade as a function f time can be written in the following way:
h = Asin(xt) + B, where:
B represets the initial height of the blade above the ground.
A represents the amplitud of length of the blade.
x represents the period.
The initial height is 35 ft, therefore, B = 35ft.
The amplotud of lenth of the blade is 10ft, therefore A = 10.
The period is two rotations every minute, therefore the period should be 60/4 = 15. Then x = 15π
Finally the equation that can be used to model h is:
h = 10sin(π15t)+35
Answer- C.) h = 10sin(π/15t)+35
Step-by-step explanation-
The equation should be equal expressed as C.) h = 10sin(π15t)+35 where 35 represents the initial height of the blade above the ground. The 15π represents the period. It is said that the blades complete two rotations every minute. Hence the period should be 60/4 equal to 15. 10 represents the amplitude of length of the blades.
What is f(g(x)) for x > 5?
f(g(x)) (you plug/substitute g(x) into x)
f(x) = 4x - √x
f(g(x)) = 4(g(x)) - √(g(x)) since g(x) = (x - 5)², you can do:
f(g(x)) = 4(x - 5)² - √(x - 5)² The ² and √ cancel each other, leaving
f(g(x)) = 4(x - 5)² - (x - 5) Next factor out (x - 5)² or (x - 5)(x - 5)
f(g(x)) = 4(x² - 10x + 25) - (x - 5) Now distribute the 4 and the -
f(g(x)) = 4x² - 40x + 100 - x + 5 Simplify
f(g(x)) = 4x² - 41x + 105 Your answer is B
ANSWER
[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]
EXPLANATION
The given functions are:
[tex]f(x) = 4x - \sqrt{x} [/tex]
and
[tex]g(x) = {(x - 5)}^{2} [/tex]
To find
[tex]f(g(x)) = f( {(x - 5)}^{2} )[/tex]
[tex]f(g(x)) =4 {(x - 5)}^{2} - \sqrt{{(x - 5)}^{2} } [/tex]
We expand and simplify to obtain,
[tex]f(g(x)) =4 {( {x}^{2} - 10x + 25)} - (x - 5)[/tex]
[tex]f(g(x)) =4{x}^{2} - 40x + 100 - x + 5[/tex]
Combine similar terms to get;
[tex]f(g(x)) =4{x}^{2} - 41x + 105 [/tex]
The correct choice is B.
what is the distance etween (-1,2) and (2,7)
Answer:
d(A,B)=square root of 34 ≈ 5.831
Answer:
[tex]\sqrt{34}[/tex]
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (2, 7)
d = [tex]\sqrt{(2+1)^2+(7-2)^2}[/tex]
= [tex]\sqrt{3^2+5^2}[/tex]
= [tex]\sqrt{9+25}[/tex] = [tex]\sqrt{34}[/tex] ← exact distance
10x² – 5x + 11 = 9x² + x + 83
Factoring Quadratics
Step-by-step explanation:
[tex]10x^2-5x+11=9x^2+x+83\qquad\text{subtract}\ 9x^2\ \text{and}\ x\ \text{and}\ 83\\\\(10x^2-9x^2)+(-5x-x)+(11-83)=0\\\\x^2-6x-72=0\\\\x^2+6x-12x-72=0\\\\x(x+6)-12(x+6)=0\\\\(x+6)(x-12)=0[/tex]
[tex]\text{The zeros:}\\\\x+6=0\qquad\text{subtract 6 from both sides}\\\boxed{x=6}\\\\x-12=0\qquad\text{add 12 to both sides}\\\boxed{x=12}[/tex]
(Tn) is an arithmetic sequence in which T3-T5=6, T4= 16 , find the (n)th term and find the order and the value of the first negative term in this sequence . Please help
Since [tex]T_n[/tex] is arithmetic, it's given recursively by
[tex]T_n=T_{n-1}+c[/tex]
where [tex]c[/tex] is a fixed number and [tex]T_1[/tex] is the starting term in the sequence. We have
[tex]T_n=T_{n-2}+2c[/tex]
[tex]T_n=T_{n-3}+3c[/tex]
and so on, so that
[tex]T_n=T_1+(n-1)c[/tex]
We're told that [tex]T_4=16[/tex], so
[tex]16=T_3+c[/tex]
and
[tex]T_5=16+c[/tex]
so that
[tex]T_3-T_5=(16-c)-(16+c)=-2c=6\implies c=-3[/tex]
Then the first term in the sequence is [tex]T_1[/tex]:
[tex]T_4=T_1+3(-3)\implies T_1=25[/tex]
and the sequence has general formula
[tex]T_n=25-3(n-1)\implies\boxed{T_n=28-3n}[/tex]
The first negative term occurs for
[tex]28-3n<0\implies28<3n\implies n>\dfrac{28}3[/tex]
[tex]\implies n=10[/tex]
The first negative term in the sequence is [tex]T_{10}=28-3\cdot10=\boxed{T_{10}=-2}[/tex].
The value of Greta's rolls of coins is $121.00. If pennies and dimes come in
rolls of 50 coins each, and nickels and quarters come in rolls of 40 coins
each, which of these combinations could Greta have?
Answer:
There are a lot of combinations possible
Step-by-step explanation:
One of them would be that each roll of quarters is $10 and each roll of pennies is 50cents so she could have 12 rolls of quarters and 2 rolls of pennies
One of the possible combinations that Greta can have is 12 rolls of quarters and 2 rolls of pennies.
What are the values of coins in USA?A penny is worth 1 cent.One nickel is equal to 5 centsOne dime is equal to 10 centsOne quarter is worth 25 centsNo. of quarters required to make $1 = 4 quarters
No. of coins in 1 roll of quarter = 40 coins = $10
If one roll of quarter is $10, then we can have 12 rolls which will give us $120.
Now we reached $120, we need $1 more to reach $121
No. of pennies to make $1 = 100 pennies
No. of coins in 1 roll of pennies = 50
So we need 2 rolls of pennies to make $1.
Hence, we need 12 rolls of quarters and 2 rolls of pennies to make $121.
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a polynomial function is shown below: f(x) = x3 - x2 - 9x + 9 which graph best represents the function ?
Answer:
The answer is C
Step-by-step explanation:
the person that made the graph is correct so it would be C
What is the approximate circumference of a circle with a radius of 60 inches use pi 3.14
Answer:
377 inches
Step-by-step explanation
C=pie x d
d= 2 x r
r= 60
d=120
pie x 120 = 376.99...
or 377
Answer:
The circumference of circle is 376.8 inches
Step-by-step explanation:
Formula:-
Circumference of circle = 2πr
Where r is the radius of circle
To find the circumference of circle
Here r = 60 inches
Circumference = 2πr
= 2 * 3.14 * 60
= 376.8 inches
Therefore the correct answer is circumference of circle with radius 60 inches is 376.8 inches
there are three questions you left blank on a multiple choice test with options A, B, C, or D. What is the probability that if you randomly guess you get at least one of them wrong?
If you left 3 blank and there's 4 options then a pretty big chance that you get it wrong....
help plz.
question:
Using the rule y=7x-5,find the value of y when x is three.
A)15
B)16
C)20
D)26
Answer: B. 16
Step-by-step explanation:
y = 7(3) - 5
y = 21 - 5
y = 16
The value of y when x is 3 is 16.
Option B is correct.
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have the Equation: y= 7x -5
Now, put the value of x =3 in the given equation and solve for y we get
So, y = 7 (3)-5
y= 21 - 5
y = 16
so, the required value is 16.
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Solve for x in the figure below. HELP ME PLEASE!!!!!
Answer:
x = 8
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the opposite interior angles
so
9x + 12 = 22 + 7x + 6
9x +12 = 7x + 28
2x = 16
x = 8
The value of x is 8 in the figure
What is interior and exterior angles?Interior angles are inside a polygon, summing to 180°. Exterior angles are outside, forming a linear pair with interior angles.
Actually, in a triangle, the sum of two interior angles is always equal to the exterior angle that is not adjacent to them. This is known as the Exterior Angle Theorem.
From the figure
<F + <G = <GHV( sum of two interior angles is equal to exterior angle)
7x +6 + 22 = 9x + 12
7x - 9x = 12- 22 -6
-2x = -16
x = -16/-2
= 8
The value of x is 8 in the figure
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If someone can do these for me that would be awesome!
Ill give lots of points
Answer:
3a. horizontal shift to the left 4 units, reflection on the x-axis
3b. vertical shift down 5 units
4. 4[tex]\sqrt{3}[/tex]
5. 3x²y²[tex]\sqrt{2x}[/tex]
6. [tex]\frac{4\sqrt{35} }{5}[/tex]
7. [tex]\frac{45-5\sqrt{7} }{74}[/tex]
8. 3√2
9. -2√7 + 5√13
10. 7√2 + 2√14
11. 10 + √15 + 2√35 + √21
12. P = 18√6 + 6√15
Step-by-step explanation:
this is gonna be a bit long but bare with me
3a. y = [tex]-\sqrt{x+4}[/tex] < -- this is a horizontal shift to the left 4 units and a reflection on the x-axis. a horizontal shift is located next to the parent function (in this case f(x) = √x). a reflection on the x-axis is located outside of the parent function.
3b. y = [tex]\sqrt{x}[/tex] - 5 < --- this is a vertical shift down 5 units. a vertical shift is located outside of the parent function
4. [tex]\sqrt{48}[/tex] to solve a radicand, we can break it up into known factors, such as numbers that are a perfect square that are factors of the number. you can create a factor tree for this, or you can do it mentally by thinking of terms.
48 can be divided by divided by 16 and 3
16 is a perfect square of 4, which goes outside of the radicand
the answer to [tex]\sqrt{48}[/tex] is 4[tex]\sqrt{3}[/tex]
5. again, to solve [tex]\sqrt{18x^5y^4}[/tex], we break it down into known factors.
lets start with 18: it can be broken down into 9 and 2, 9 is a perfect square of 3
so far the radicand looks like this: 3[tex]\sqrt{2x^5y^4}[/tex]
next we will break down [tex]x^5[/tex]. looking at the exponent, we can see that we have a perfect square in the exponent, which is 4. the square root of 4 is 2. we would leave the leftover x in the radical as it is not a perfect square, and put x² on the outside as it is a result of the perfect square
3x²[tex]\sqrt{2xy^4}[/tex]
finally lets look at [tex]y^4[/tex]. we see that the exponent is a perfect square, 4. the square root of 4 is 2, so y² would go on the outside, and no y terms would be left on the inside. the final radical looks like this:
3x²y²[tex]\sqrt{2x}[/tex]
6. [tex]\frac{4\sqrt{7} }{\sqrt{5} }[/tex]
to solve this, we would need to rationalize the denominator by getting rid of the radical in the denominator. to do this we would multiply the expression by [tex]\sqrt{5}[/tex] and we would get:
[tex]\frac{4\sqrt{35} }{5}[/tex]
we cannot simplify this any further, so this would be our answer
7. [tex]\frac{5}{9 + \sqrt{7} }[/tex] like the last question, we need to get rid of the square root in the denominator by multiplying the entire expression by [tex]9 - \sqrt{7}[/tex]. we get:
[tex]\frac{5(9-\sqrt{7}) }{(9+\sqrt{7})(9-\sqrt{7}) }[/tex]
the denominator can be multiplied together to get 81 - 7 = 74, and in the numerator we get 5(9-√7) which can be distributed as 45 - 5√7. in total we get:
[tex]\frac{45-5\sqrt{7} }{74}[/tex] this cannot be simplified any further, so this is the answer
8. 3√50 - 3√32 to solve, we need to get the same radical. to do this, we can break each radical up into known terms. √50 can be simplified as 25 and 2. 25 is a perfect square, and is equal to 5. √50 = 5√2
3(5√2) = 15√2
we can break up √32 as 16 and 2. 16 is a perfect square which is equal to 4. √32 = 4√2
-3(4√2) = -12√2
the expression looks like this: 15√2 - 12√2 < subtract normally and we get 3√2 <-- this is our final answer, and we cannot simplify further
9. 2√7 - 4√13 -4√7 + 9√13 < we can combine like terms by adding/subtracting
2√7 -4√7 = -2√7
-4√13 + 9√13 = 5√13
-2√7 + 5√13 this cannot be simplified further, so this is the answer
10. √7(√14 + 2√2) < distribute √7 into the expression
√7 × √14 = √98 = 7√2
√7 × 2√2 = 2√14
the answer is 7√2 + 2√14
11. (√5 + √7)(√20 + √3) < to solve, we can FOIL this out
(√5 + √7)(√20 + √3) = 10
(√5 + √7)(√20 + √3) = √15
(√5 + √7)(√20 + √3) = 2√35
(√5 + √7)(√20 + √3) = √21
we get the following expression: 10 + √15 + 2√35 + √21, we cannot simplify this further so this is our answer
12. the perimeter of a rectangle is P = 2l + 2w. we are given the width 3√6 + 4√15 and the length 6√6 - √15. plugged into the formula we have:
2(3√6 + 4√15) + 2(6√6 - √15) < distribute 2 into each expression:
(6√6 + 8√15) + (12√6 - 2√15) < combine like terms, as in combine terms with like radicals
6√6 + 12√6 = 18√6
8√15 - 2√15 = 6√15
P = 18√6 + 6√15
we cannot simplify this further, so this is the answer
hope this helped!
Which scenario can be represented using the inequalities below?
1.25 < x < 1.5
A container of milk costs at least $1.25 but less than $1.50.
A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
The point value of a test item is more than 1.25 points and less than 1.5 points.
Answer:
I would go with a container of milk costs at least $1.25 but less than $1.50.
Answer: Fourth option is correct.
Step-by-step explanation:
Since we have given that
[tex]1.25<x<1.5[/tex]
The point value of a test item is strictly more than 1.25 points and strictly less than 1.5 points.
According to options:
It can be represented as :
The point value of a test item is more than 1.25 points and less than 1.5 points.
All other options except the above is not satisfying the above inequality.
Hence, Fourth option is correct.
Plz help me with this
The answer is B. Since there are no parenthesis around pi/2, it stating that the graph shifts up pi/2 units - which is incorrect. It is a phase shift of pi/2 units (not a vertical shift).
Answer: [tex]\bold{B)\quad y=2\ sin2x+\dfrac{\pi}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The standard form of a sine equation is: y=A sin(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]
In the given graph,
A (amplitude) = 2 Phase Shift [tex]\bigg(\dfrac{C}{B}\bigg)[/tex] = [tex]\dfrac{\pi}{2}[/tex] to the left P (period) = π --> B = 2 D (vertical shift) = 0Option B shows the value of D as [tex]\dfrac{\pi}{2}[/tex], which is incorrect since there is no vertical shift up. If the parenthesis included that value, like Option C, then it would have been correct.
Every year the population of students in a certain school district is recorded. In 2014, MVCSD had a population of 7,895 students. By 2018, the population of students had increased by approximately 28%. How many students were recorded in the MVCSD in 2018?
Answer:
[tex]\boxed{2211}[/tex]
Data:
Population in 2014 = 7895
% increase = 28 %
Calculations:
28 % = (Increase/Original number) × 100 %
28 = (Increase/7895) × 100
28/100 × 7895 = Increase Multiplied each side by 7895/100
Increase = 2211
[tex]\boxed{ 2211}[/tex] students were recorded in the MVCSD in 2018.
What is the solution of 9x-8=34x-12
The equation 9x-8=34x-12 is a linear equation which is solved by moving variables and numerals at the opposite sides of the equation. This simplifies to -25x = 4 and by dividing both sides by -25, the answer x=-0.16 is obtained.
Explanation:The subject of your question is a linear equation, more specifically, the solution to the equation 9x-8=34x-12. To find the solution, firstly bring variables to one side and numerals to the other side of the equation. So, it becomes 9x - 34x = 12 - 8, which simplifies to -25x = 4.
Then, solve for 'x' by dividing both sides by -25. This yields x = -4/25 or x = -0.16. So, x=-0.16 is the solution to the original equation 9x-8=34x-12.
Such questions involve understanding the principles of algebraic manipulation and the resolution of linear equations, which are fundamental concepts in mathematics.
Learn more about Linear Equations here:https://brainly.com/question/32634451
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ASAP, The following parallelogram is reflected over the x-axis and then reflected over the y-axis. What are the coordinates of the vertices of the image?
(2, 1), (1, -1), (-2, -1), (-1, 1)
(1, 2), (-1, 1), (-1, -2), (1, -1)
(1,1), (2, -1), (-2, 1), (-1, -1)
(1, 1), (-1, 2), (1, -2), (-1, -1)
Answer:
(1,1), (2,-1), (-2,1), (-1,-1)
Step-by-step explanation:
Red Line: over x-axisBlue Line: over y-axis