Answer:
80cm^2/s
Step-by-step explanation:
This is a related rates problem where we are considering the rate at which the area of a square changes with respect to time.
So lets consider the area of a square:
A = s^2 (where s represents the length of one side of the square)
Related rates problem deal with functions of time so if we take the area and side length as a function of time and then differentiate implicitly we get:
[tex]\frac{dA}{dt} = 2s(\frac{ds}{dt})[/tex]
The problem states that the side of a square is increasing at a rate off 8cm/s so we can conclude that ds/dt = 8cm/s leaving us with:
[tex]\frac{dA}{dt} = 16s[/tex]
Now, to solve for s we have to consider the other value given. If the area of the square is initially 25cm^2 we can plug this into our formula for area to solve for the side length.
25 = s^2
s = +/- 5 (since side lengths are only positive we only consider +5)
s = 5
Now we can plug this back in for s:
[tex]\frac{dA}{dt} = 80[/tex]
Therefore, the rate at which the area of the square is increasing is 80cm^2 per second.
How would I solve this ?
1. Use the Multiplication Distributive Property: (xy)^a = x^a y^a
3√6 3√x √y^2
2. Use this rule: (x^a)^b = x^ab
3√6 3√xy^2/3
Rasie 2 to the 4th power then find the difference
Rishi is making a map of a remote village. In this village, each hut has a rectangular base measuring
4
m
4 m4, start text, space, m, end text by
6
m
6 m6, start text, space, m, end text.
Move the points on the grid below to draw the base of one of the huts described above.
The required dimensions of the hut base will be 8 by 12 m.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that Rishi is making a map of a remote village. In this village, each hut has a rectangular base measuring 4 m by 6 m.
Move the points on the grid below to draw the base of one of the huts described above.
As shown in the above figure, just move the top two points down two spaces. Two sides take up four, and the other two take up six. we can find that the length of the hut base is 12 m and the width 8 m.
Therefore, the required dimensions of the hut base will be 8 by 12 m.
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2. Doug paid $39.95 for dinner. He left a 15% tip for the server. Which of the following is closest to
the tip left by Doug? *
Answer:
$5.99
Step-by-step explanation:
In this problem, Doug paid the following amount for the dinner:
[tex]p=\$39.95[/tex]
He also left a 15% tip.
Here we want to calculate what is the amount correspondant to the tip.
In order to find this value, we have to calculate the 15% of the value of the dinner, therefore we want to find
the 15% of 39.95$
The percentage (15%) can be rewritten as fraction:
[tex]15\% =\frac{15}{100}[/tex]
Therefore, the amount of the tip is
[tex]t=\frac{15}{100}p[/tex]
And substituting p, we find:
[tex]t=\frac{15}{100}(\$39.95)=\$5.99[/tex]
So, the tip is $5.99.
Answer: 5.99
Step-by-step explanation:
Change % to decimal
Then multiply
15% =.15
39.95 x .15 = 5.99
Which statement below is true?
A. If p → q is true, then q → p is true.
B. If p → q is true and p is true, then q is true.
C. If p → q and q → r are true, then q → p is true.
D. If p → q and q → r are true, then r → p is true.
The correct statement is B. If p → q is true and p is true, then q is true.
Explanation:The correct statement is B. If p → q is true and p is true, then q is true.
This is known as the modus ponens rule and is a valid argument form in propositional logic. It states that if an implication is true and the antecedent (p) is true, then the consequent (q) must also be true.
For example, if p represents 'it is raining' and q represents 'the ground is wet', and the statement 'if it is raining, then the ground is wet' is true, and we know that it is indeed raining (p is true), then we can conclude that the ground is wet (q is true).
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A. Quotient
B. Difference
C. Product
D. Sum
Answer: product
Step-by-step explanation:
product means that you are multiplying
[tex]\pi r * r = \pi r^{2}[/tex]
Four CDs and 4 DVDs cost $164. The cost of the 4 CDs is half the cost of the
4 DVDs. What is the cost of each CD?
Which of the following problems would help you solve the problem above?
Answer:
Each CD cost $20.50
Step-by-step explanation:
You would divide the cost of the DVDs by 4: 164÷4=41
Now the CDs are half the cost of the DVDs so you would divide 41 by 2: 41÷2=20.50
Your answer would be $20.50
The ordered pairs below represent a relationship between x and y.
Answer:
Step-by-step explanation:
3 halves times the product of 3 1 fifth
Answer: 48/10 , if you need it simpflity then its 4 and four fifths ( 4 4/5 )
Find an equation in slope-intercept form of the line that has slope 2 and passes through point A(-8, 7)
Answer:
y = 2x + 23
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2, thus
y = 2x + c ← is the partial equation
To find c substitute (- 8, 7) into the partial equation
7 = - 16 + c ⇒ c = 7 + 16 = 23
y = 2x + 23 ← equation of line
Answer:
y=mx+c
y=2x+c
Y intercept(c) 23 - to find y we have to input the values
7=2*-8+c
7=-16+c
23=c
If m∠NOP = 24° and m∠NOQ = 110°, what is m∠POQ?
Two adjacent angles, angle NOP and angle POQ.
A. 62°
B. 86°
C. 134°
Correct answer for the above question is - option B. 86°
Step-by-step explanation:
Given:
∠NOP = 24°
∠NOQ = 110°
∠NOP and ∠POQ are adjacent angles
To Find:
∠POQ = ?
Solution:
Hereby, we can say that ∠POQ lies between line OQ and ON as given (∠NOP and ∠POQ are adjacent angles )
∠NOQ - ∠NOP = ∠POQ
∠POQ = 110° - 24°
∠POQ = 86°
Angle POQ is 86°
Thus we can conclude option B as correct answer.
The measure of the angle POQ is 86°
From the question, we are given the following parameters;
Given:
∠NOP = 24° ∠NOQ = 110° ∠NOP and ∠POQ are adjacent anglesRequired
∠POQ = ?
To get the unknown angle ∠POQ, we will use the expression below:
∠NOQ - ∠NOP = ∠POQ
∠POQ = 110° - 24°
∠POQ = 86°
Therefore the measure of the angle POQ is 86°
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One more than 3 times a number is
the same as 5 times the number,
decreased by 15. Find the number
Answer: the number is 8. hope it helps please give me brainliest!
Step-by-step explanation:
so the equation is 1+3x=5x-15 x= the number
-1 from both sides
3x=5x-16
-5x from both sides
-2x=-16
divide both sides by -2 to get x by itself
x=8
What is the exact value of tan(3009)?
Answer:
-sqrt(3)
Step-by-step explanation:
If you type in your calculator, you'll get -1.732050808... which is the negative of sqrt(3)
Which percent is equivalent to 720?
Answer:
720%
Step-by-step explanation:
it was easy cant explain
Answer: Its 35%
Step-by-step explanation: I'm assuming you mean 7/20
Marisol is solving the equation 6(x+3)=21. Find her mistake and correct it.
Answer:
x = 1/2, See Explanation Below
Explanation:
When you solve the equation, you have to take out the 6 first. The mistake is that you Marisol subtracted from 3 directly instead of factoring the x and the 3 out. Below is what you are supposed to do in order to get the right solution.
Step-by-step for Equation:
6(x+3) = 21
6x + 18 = 21
6x = 21 - 18
6x = 3
x = 3/6
x = 1/2
I hope this helps! If you are kind enough, please give me the brainliest answer. It is greatly appreciated if so. Thank You!
how do you find volume of a octagonal prism?
Answer:
V=2(1+2)a2h
Step-by-step explanation:
Final answer:
To calculate the volume of an octagonal prism, find the area of the base using the formula A = 2(1 + √2)s² for a regular octagon, then multiply by the prism's height. Ensure all measurements are in the same units.
Explanation:
To find the volume of an octagonal prism, you need to calculate the area of the base octagon and then multiply it by the height of the prism. The formula for the area of a regular octagon (assuming all sides, s, are equal) is [tex]A = 2(1 + \sqrt{2} )s^2[/tex], where s is the length of one side. To find the volume, V, you then multiply this area by the height, h, of the prism: V = A*h = [tex]2(1 + \sqrt{2} )s^2*h[/tex]. It's important to ensure that all measurements are in the same units to get the volume in cubic units (e.g., cubic centimeters, cubic meters).
What is the perimeter of the isosceles triangle shown below?
A) 27 units
B) 22 units
C) 32 units
D) 24 units
The perimeter of the isosceles triangle is C) 32 units.
Step-by-step explanation:
Step 1; First, we plot the three ends of the triangle. Assume the bottom left is A, the bottom right is B and the top end is C. The coordinates are;
A = (-6, -2), B = (6, -2) and = C (0, 6). A triangle's perimeter is the sum of its three side lengths. So we need to determine the side lengths of the given sides.
Step 2; To find the distance between A (-6, -2) and B (6, -2), we use the formula
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between (-6, -2) and (6, -2) where (-6, -2) is (x1, y1) and (6, -2) is (x2, y2).
Distance = √ (6 - (-6))² + (2 - (-2))² = √ 12² + 0² = √12² = 12 units.
Step 3; To find the distance between C (0, 6) and B (6, -2), we use the formula
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between (0, 6) and (6, -2) where (0, 6) is (x1, y1) and (6, -2) is (x2, y2).
Distance = √ (6 - 0)² + (-2 - 6)² = √ 6² + 8² = √36 + 64 =√100 = 10 units.
Step 4; To find the distance between C (0, 6) and A (-6, -2), we use the formula
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between (0, 6) and (-6, -2) where (0, 6) is (x1, y1) and (-6, -2) is (x2, y2).
Distance = √ (-6 - 0)² + (-2 - 6)² = √ 6² + 8² = √36 + 64 =√100 = 10 units.
Step 5; The perimeter of the triangle = 12 + 10 + 10 = 32 units, which is option C.
What is the equation of a circle with center (2,-8) and radius 9?
Answer:
9^2= (x+2)^2+(y+8)^2
Step-by-step explanation:
The equation is r^2=(x+h)^2+(y-k)^2
Answer:
x2+y2-4x+16y-13
Step-by-step explanation:
center (h,k)=2,-8
radius(r)=9
we know
(x-h)2+(y-k)2=r2
now insert above given information
(x-2)2+(y+8)2=9×9
Yuko is making pancakes. The double number line shows the ratio flour:eggs. If yuko accidentally uses 3 eggs instead of 2 eggs, how much flour should he use?
Answer: Since Yuko used 1.5x the amount of eggs that he should have used, in order to find the answer you need to take the amount of flour Yuko was SUPPOSED to use and multiply it by 1.5
If Yuko uses 3 eggs instead of 2, Yuko should multiply the amount of flour required by 3/2 or 1.5 to maintain the correct proportionality, according to the recipe's proportions.
Explanation:Based on the problem, we are dealing with ratios in a recipe. The ratio provided is flour to eggs. If we had an example ratio, let's say 2 cups flour to 1 egg, and Yuko uses 3 eggs instead of 1, we'd have to scale up the flour by the same factor to keep the proportions in the pancake batter consistent.
Since Yuko uses three times the eggs (3 is three times larger than 1), he should also use three times the amount of flour. So for our example, if 1 egg needed 2 cups of flour, 3 eggs (which is three times 1 egg) would require 6 cups of flour (three times 2 cups) to maintain the correct proportionality.
Thus, if Yuko accidentally uses 3 eggs instead of 2 eggs, he needs to also increase the amount of flour used proportionately to maintain the same pancake consistency according to the recipe's ratios.
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I am greater than 1/3 but less than 1. My numerator and denominator have a difference of 5 and a product of 24. Who am I?
Answer:
Step-by-step explanation:
5/8
how do i write this decimals 56.01 in expanded form
Answer: sowwy if im wrong
Expanded Numbers Form:
50
+6
+0
+0.01
Step-by-step explanation:
Expanded Numbers Form:
50
+6
+0
+0.01
Expanded Factors Form:
5*10
+6*1
+0*0.1
+1*0.01
Expanded Exponential Form:
5*101
+6*100
+0*10-1
+1*10-2
The expanded form of 56.01 is 50 + 6 + 0.01.
To write the decimal 56.01 in expanded form, we break down each digit's place value.
56.01 can be expressed in expanded form as follows:
50 + 6 + 0.01
The place values are as follows:
50 (50 is in the tens place, and we can also write it as 5 * 10)
6 (6 is in the ones place, and it is just 6)
0.01 (0.01 is in the hundredths place, and we can also write it as 1/100)
So, the expanded form of 56.01 is 50 + 6 + 0.01.
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Find the rate of change of the function
15x - 5y=20
Answer:
3
Step-by-step explanation:
⇒15x-20=5y
⇒(15x-20)/5=y
⇒3x
The rate of change of the function is 3
m = 3how to find the rate of change of the functionTo find the rate of change of the function 15x - 5y = 20, we need to solve for y in terms of x and then determine the coefficient of x, which represents the rate of change.
Let's solve the equation for y:
15x - 5y = 20
Subtract 15x from both sides:
-5y = -15x + 20
Divide both sides by -5:
y = (15/5)x - 4
Simplifying the equation:
y = 3x - 4
Now we can observe that the coefficient of x is 3. Therefore, the rate of change of the function is 3. This means that for every unit increase in x, the corresponding y-value increases by 3.
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given h(x) = 4x + 3, find h(-1)
Answer:
-1
Step-by-step explanation:
4x-1=-4
-4+3=-1
The value of h(-1) is -1 after plugging the value of x = -1 in the function h(x) = 4x + 3 the answer is -1.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function h(x) = 4x + 3
Plug x = -1 in the above function:
h(-1) = 4(-1) + 3
h(-1) = -4 + 3
h(-1) = -1
The linear function can be defined as the relation between two variables, if we plot the graph of the linear function we will get a straight line.
If in the linear function, one variable is present, then the function is known as the linear function in one variable.
Thus, the value of h(-1) is -1 after plugging the value of x = -1 in the function h(x) = 4x + 3 the answer is -1.
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A line is perpendicular to y = - x-1
and intersects the point (6,9).
What is the equation of this
perpendicular line?
Answer:
y=x+3
Step-by-step explanation:
y=-1x-1..... k1=-1
k1*k2=-1 (perpendicular) then
Slope=1=k2
A(6,9) x1 =6,y1 =9
y-y1 =k2(x-x1)
y-9=1(x-6)
y-9=x-6
y=x-6+9
y=x+3
(−3x − 6)(3x2 − 6x + 3)????
Answer:
-216
Step-by-step explanation:
(−3x − 6)(3x2 − 6x + 3)
=(18)(6 − 6x + 3)
=(18)(6 − 18)
=(18)(− 12)
= -216
Answer:
-9 • (x + 2) • (x - 1)2
Step-by-step explanation:
(-3x-6)(3x2-6x+3)
Final result :
-9 • (x + 2) • (x - 1)2
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(-3x - 6) • ((3x2 - 6x) + 3)
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-3x - 6 = -3 • (x + 2)
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
(3x2 - 6x + 3) = 3 • (x2 - 2x + 1)
Trying to factor by splitting the middle term
4.2 Factoring x2 - 2x + 1
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 1 • 1 = 1
Step-2 : Find two factors of 1 whose sum equals the coefficient of the middle term, which is -2 .
-1 + -1 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and -1
x2 - 1x - 1x - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
Add up the last 2 terms, pulling out common factors :
1 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-1)
Which is the desired factorization
Multiplying Exponential Expressions :
4.3 Multiply (x-1) by (x-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-1) and the exponents are :
1 , as (x-1) is the same number as (x-1)1
and 1 , as (x-1) is the same number as (x-1)1
The product is therefore, (x-1)(1+1) = (x-1)2
Final result :
-9 • (x + 2) • (x - 1)2
solve for x
x/9=7
i need help
Answer:
x = 63
Step-by-step explanation:
Step 1: Solve for x by multiplying both sides by 9
x/9 * 9 = 7 * 9
x = 63
Answer: x = 63
Find the sum of the first 8 terms in the following geometric series.
Do not round your answer. 2+8+32+...
The sum of 8 terms is 43690.
What of series?A series is the cumulative sum of a given sequence of terms.
Given:
2+8+32+...
a=2. r= 4
So, the sum of 8 terms
Sn = a(r^n - 1) / (r - 1),
S8 = 2( 65536 -1)/ (4-1)
S8= 65535*2/
S8 = 43690.
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Joey is organizing his toys so that each bin has the same number of toys without mixing the toys. He has 27 trucks and 36 boats. What is the greatest number of toys that can be put in a bin?
In the problem, we need to find the greatest common factor (GCF) of 27 and 36, which are the number of toys Joey has. The GCF is the highest number that can divide two numbers without a remainder. Factoring out, we see that the GCF is 9, and thus, Joey can put 9 toys in each bin.
Explanation:The subject of this question is Mathematics, specifically the area of greatest common factor (GCF). We have to find the greatest number of toys that can be evenly distributed in bins using 27 trucks and 36 boats.
To solve this problem, we need to determine the GCF of 27 and 36. The GCF is the largest number that can divide two numbers without a remainder. Factoring out 27 and 36, we find that their common factors are 1, 3, and 9, with 9 being the largest. Therefore, the greatest number of toys Joey can put in a single bin without mixing the toy types is 9.
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What is s in 2m+4s=16 if m=-2
Answer:
s = 5
Step-by-step explanation:
2m + 4s = 16
Step 1: Plug in -2 for m
2(-2) + 4s = 16
-4 + 4s = 16
Step 2: Solve for s
-4 + 4s + 4 = 16 + 4
4s / 4 = 20 / 4
s = 5
Answer: s = 5
Answer:
s= 5
Step-by-step explanation:
s= 5
m= - 2
2m + 4s= 16
Replace the m with the value it is in brackets. Remember brackets mean to multiply.
2(-2) + 4s= 16
-4 + 4s= 16
Carry over the -4 and make s the subject.
4s= 16 - - 4
4s= 16 + 4
4s= 20
s= 20/4
s= 5
Therefore s= 5
To check if the answer was correct, replace the s and m with the value it is in brackets. s= 5; m= 2
2(-2) + 4(5)= 16
-4 + 20 = 16
Therefore s= 5 and the answer is correct!
What is 19/22 as a decimal rounded to the nearest tenth
Final answer:
19/22 as a decimal is approximately 0.86363636..., and when rounded to the nearest tenth, it is 0.9.
Explanation:
To find what 19/22 is as a decimal rounded to the nearest tenth, we first need to perform the division of 19 by 22. When you carry out this division, the result is approximately 0.86363636... To round this to the nearest tenth, we would look at the first digit after the decimal point, which is 8, since the next digit (6) is greater than or equal to 5, we round up the 8 to 9. Therefore, 19/22 rounded to the nearest tenth is 0.9.