Answer:
30x100= 3000
Step-by-step explanation:
Consider the function f,g:[tex]\mathbb{R} \to\mathbb{R}[/tex] defined by
[tex] \rm f(x) = {x}^{2} + \frac{5}{12} \: and \: g(x) = \begin{cases}2 \bigg( \rm 1 - \dfrac{4 |x| }{3} \bigg), \: \: \: \: |x| \leq \dfrac{3}{4}, \\ \\ 0, \: \: \: \: \: \rm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: |x| > \dfrac{3}{4} .\end{cases} [/tex]
If [tex]\alpha[/tex] is the area of the region
[tex] \rm \bigg \{(x,y) \in \mathbb{R} \times \mathbb R : |x| \leq \dfrac{3}{4} ,0 \leq y \leq min \{f(x),g(x) \} \bigg \}[/tex]
then the value of 9[tex]\alpha[/tex]
Suppose [tex]x>0[/tex]; then the curves meet when
[tex]x^2 + \dfrac5{12} = 2 - \dfrac83 x \implies x^2 + \dfrac83 x - \dfrac{19}{12} = \left(x + \dfrac{19}6\right) \left(x - \dfrac12\right) = 0 \\\\ \implies x = \dfrac12[/tex]
By symmetry, they intersect at [tex]x=\pm\frac12[/tex].
We also see that [tex]\min\left\{f(x):|x|\le\frac34\right\} = \frac5{12}[/tex] and [tex]\max\left\{g(x):|x|\le\frac34\right\} = 2[/tex] at [tex]x=0[/tex]. [tex]f[/tex] and [tex]g[/tex] are continuous, so it follows that
[tex]\min\left\{f(x),g(x) :|x|\le\frac34\right\} = \begin{cases} f(x) & \text{if } |x| < \frac12 \\ g(x) & \text{if } |x| > \frac12 \\ f\left(\pm\frac12\right) = g\left(\pm\frac12\right) = \frac23 & \text{if } x = \pm\frac12 \end{cases}[/tex]
Compute the area [tex]\alpha[/tex]. Taking advantage of symmetry again, we have
[tex]\alpha = \displaystyle 2 \int_0^{1/2} \int_0^{f(x)} dy\,dx + 2 \int_{1/2}^{3/4} \int_0^{g(x)} dy \, dx \\\\ ~~~~ = 2 \int_0^{1/2} f(x) \, dx + 2 \int_{1/2}^{3/4} g(x) \, dx \\\\ ~~~~ = \left. 2 \left(\frac{x^3}3 + \frac{5x}{12}\right) \right\vert_0^{1/2} + \left. 2 \left(2x - \frac{8x^2}6\right) \right\vert_{1/2}^{3/4} \\\\ ~~~~ = \left(\frac12 - 0\right) + \left(\frac32 - \frac43\right) = \frac23[/tex]
and it follows that [tex]9\alpha = \boxed{6}[/tex].
Find two positive numbers whose difference is 7 and whose product is 800.
Answer:
25 and 32
Step-by-step explanation:
32 - 25 = 7
32 x 25 = 800
please help for brainiest asap!!!
The first mistake in solving the given algebraic expression is; Line 3
How to solve Algebraic Expressions?We are given the algebraic expression as;
6(2y + 6) = 4(9 + 3y)
The first step would be to use distributive property of algebra to expand the bracket to get;
12y + 36 = 36 + 12y
The next step will be to use subtraction property of equality to subtract 36 from both sides to get;
12y = 12y
Now, since the coefficients of the variable is the same on both sides, then it means the equation has no solution and as such the conclusion is that the first mistake is in line 3.
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0.02,0.2,2,20,200, what is next
Answer:
0.2
Step-by-step explanation:
Answer: 2000
Step-by-step explanation:
The pattern is multiplying by 10. Therefore, 200 x 10= 2000
. The sides of a rectangle are (x+1) and (2x +5). If the perimeter is 36m, Find the value of x
what is the unit digits of 3^40
Answer:
1
Step-by-step explanation:
the answer is 1.21576655000000000.
the unit of this no. is 1.
There are 5,000 nails in five boxes. The first and second boxes have 2,700 nails altogether. The second and third boxes have 2,000 nails altogether. The third and fourth boxes have 1,800 nails altogether. The fourth and fifth boxes have 1,700 nails altogether. How many nails are in each box?
There are 5,000 nails in five boxes. The first and second boxes have 2,700 nails altogether. The second and third boxes have 2,000 nails altogether. The third and fourth boxes have 1,800 nails altogether. The fourth and fifth boxes have 1,700 nails altogether. How many nails are in each box
Purchases of both small and large boxes total:
two little boxes.
six huge boxes
Two equations must be created with the given data in order to answer the unknowns:
150X + 400Y = 2700 (the price of the boxes and the total number of nails, where X is the small boxes and Y the large boxes)
Y = 3X
Equation one is then changed to equation 2, and variable X is eliminated:
150X + 400 (3X) = 2700
150X + 1200X = 2700 1350X = 2700 X = 2700/1350 X = 2
In order to determine the number of big boxes, equation 2's value of X is finally changed:
Y = 3X
Y = 3
Y = 6
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Alex, Bob and Carl go for a walk every day. If Alex doesn't wear a hat, then Bob wears
a hat. If Bob doesn't wear a hat, then Carl wears a hat. Today Bob is not wearing a hat.
Who is wearing a hat?
Answer:
Carl and Alex are wearing hats.
Step-by-step explanation:
If Bob doesn't isn't wearing a hat, then Carl is, so Carl clearly is wearing a hat.
Now let's look at Alex. If he wasn't wearing a hat, then Bob would be wearing one. (If Alex doesn't wear a hat, then Bob wears
a hat). The logical conclusion is that Alex must be wearing a hat as well.
80% of the frogs in a pond are spring peepers. If there are 200 frogs in the pond, how many spring peepers are there?
Answer:
160
Step-by-step explanation:
If 80% of the frogs in a pond are spring peppers, and there are 200 frogs in the pond, to find how many spring peppers are in the pond, find 80% of 200.
[tex]\begin{aligned} \sf \implies 80\% \textsf{ of }200 & = \sf 80\% \times 200\\\\& = \sf \dfrac{80}{100} \times 200\\\\& = \sf \dfrac{80}{100} \times \dfrac{200}{1}\\\\& = \sf \dfrac{80 \times 200}{100 \times 1}\\\\& = \sf \dfrac{16000}{100}\\\\& = \sf 160\end{aligned}[/tex]
Therefore, there are 160 spring peppers in the pond.
19. 9a2b = c + 4a, for a
Answer:x/5 + 2b/5
Step-by-step explanation:
9a-2b=c+4a solve for a
9a-2b=c+4a
add -4a to both sides
9a-4a-2b=x+4a-4a
5a-2b=x
add 2b to both sides
5a-2b+2b=x+2b
5a= x+2b
divide by 5
5a/5 = x/5 +2b/5
a= x/5 + 2b/5
I don't understand someone please help. :(
Answer:
d I'm leaning towards d
Step-by-step explanation:
a doesn't make sense B can't be because we went adding d is phrased wrong
What is the measurement of this angle ?
The measurement of the given angle is a 90 degree.
According to the statement
We have to find that the measurement of this angle.
So, For this purpose, we know that the
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
From the given information:
In the given figure, the measurement of the angle we have to find.
A 90-degree angle is a right angle and it is exactly half of a straight angle. It always corresponds to a quarter turn.
And from the figure it is clearly visible that the line of the angle exactly matches with the 90 degree.
Then the angle is 90 degree.
So, The measurement of the given angle is a 90 degree.
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Name the intersection of line AB and line CB
Answer:
B
Step-by-step explanation:
I am not sure what kind of help you need here. the answer is kind of obvious, already revealed by the names of the lines (AB and CB). they meet or intersect at their joined point B.
A production assistant must divide a page of text into two columns. If the page is 6 3/4 inches wide, how wide will each column be
The width of each column is 3.375.
According to the statement
We have to find that the width of the each column.
So, For this purpose, we know that the
Width is the the horizontal measurement taken at right angles to the length.
In other words, It is the distance from one side to the other side which measures across a particular shape or object whose lengths are forming right angles with the sides as in the case of a rectangle.
From the given information:
A production assistant must divide a page of text into two columns. If the page is 6 3/4 inches wide.
Then
width of the page = 27/4 inches
And the number column is divided into page = 2
Then
The width of column = width of the page/ column in a page
The width of column = 27/4/ 2
The width of column = 6.75/ 2
The width of column = 3.375.
So, The width of each column is 3.375.
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[tex]-6y + 4 = | 4y + 12 |[/tex]
Answer: its not equal.
Step-by-step explanation:
-6y + 4 = 2 (-3y + 2)
|4y + 12| = 4 (y + 3)
How can you round 493 and 917 to the underlined number
The rounding off a number of 493 is 490 and The rounding off a number of 917 is 920.
Rounding off number:
1)Round the number up if 5, 6, 7, 8, or 9 follow the number you are rounding.
2)Round the number down if the rounded number is followed by a 0, 1, 2, 3, or 4.
The given numbers are 493 and 917
The rounding-off number of 493 is
⇒493, The last number is 3, need to decrease and round off⇒490
The rounding-off number of 917 is
⇒917, The last numberis 7, need to increase and round off⇒920
Therefore, The rounding off a number of 493 is 490 and The rounding off a number of 917 is 920.
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The perimeter of any rectangle in which the length is 4 more than twice the width is P = 6 w + 8 , where w is the width. Which formula can be used to find the width given the perimeter? Multiple choice question. cross out A) w = P − 4 3 cross out B) w = 1 6 P − 8 cross out C) w = − P + 8 6 cross out D) w = P − 8 6
Answer: option D
Step-by-step explanation:
Given equation:
P = 6 w + 8 [eq1]
l=2w+4 [where l is length]
using eq1 we have:
6w=P-8
w=(P-8)/6
hence option D
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2/9=?/18=?/27 help pleace thank u so much
Answer:Not there yet
Step-by-step explanation: Think about it your close 2/9 = nothing why do numbers determine our grades so don't answer if anything flunk out of school
If you have only $50, can you afford to buy a pair of shoes marked $69.99?
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 38 ft/s. The ball's height h (in feet) after / seconds is given by the following.
h=2+38t-16t^2
Find all values off for which the ball's height is 16 feet.
The height of the ball according to the function h(t) is 16 feet after 1.92 seconds and after 0.46 seconds.
A function is defined as a expression containing one or more variables.
Technically speaking, a function is a means of linking a set of inputs to a set of outputs.
The height of the ball at any time t is given by the function:
[tex]h(t)=-16t^2+38t+2[/tex]
Now the required height of the ball(in feet) is 16 feet. We have to find the value of t for which h(t)=16.
Let us substitute the values:
[tex]\implies h(t)=-16t^2+38t+2\\\implies 16=-16t^2+38t+2\\\implies 16t^2-38t+14=0\\\implies 8t^2-19t+7=0[/tex]
This is in the form of a quadratic equation in t.
Solving by using the quadratic formula:
We know that for a quadratic equation [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Therefore for the above quadratic equation:
[tex]t=\frac{-(-19)\pm \sqrt{(-19)^2-4(8)(7)}}{2(8)}\\t=\frac{19+\sqrt{137}}{8},t=\frac{19-\sqrt{137}}{8}\\t=1.919...,t=0.455...[/tex]
Therefore the ball reaches the height of 16 feet at times 1.92 seconds and at 0.46 seconds.
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Translate the sentence into an equation.
Six more than the quotient of a number and 4 is equal to 8.
Use the variable x for the unknown number.
Answer:
(n ÷ 4) + 6 = 8
Step-by-step explanation:
Pretty sure I answered this before, but here you go.
Quotient means The answer when you divide' So we are working in the division.
n ÷ 4 is the division part
It says 'and' which can also mean addition. So we add 6. So far our equation is: (n ÷ 4) + 6 (Brackets are needed as we are dividing n by 4 and not dividing n by 4+6)
Lastly it says the answer must be 8 so we add that at the end. So the answer is:
(n ÷ 4) + 6 = 8
-12[tex]-12\ \textless \ \frac{1}{2}\left(4x+16\right)\ \textless \ 18[/tex]
The solution to the given inequality is -10 < x < 5.
How to solve a compound inequality involving the and operation?
To solve a compound inequality involving the and operation, we solve each inequality, then find the intersection of these solutions.
For this problem, the inequality is given by:
-12 < 0.5(4x + 16) < 18.
Multiplying all the terms by 2:
-24 < 4x + 16 < 36
Hence:
4x + 16 > -24
4x > -40
x > -10.
4x + 16 < 36
4x < 20
x < 5
The intersection of these two solutions is:
-10 < x < 5.
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27. If Q is the midpoint of PR, find the coordinates of R if
P (3,-5) and Q (-1,2)?
Answer: -5,9
Step-by-step explanation:
find the domain of the following functions and simplify their expressions.
The domain of the function is (-∞,∞) and the simplified expression is x²-6x-40 .
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.
The given functions are
f(x)=6x+24
g(x)=x²-16
Now we have to find (g-f)(x) .
(g-f)(x)=x²-16-6x-24
or,(g-f)(x)=x²-6x-40
or,(g-f)(x)=x²-10x+4x-40
or,(g-f)(x)=x(x-10)+4(x-10)
or,(g-f)(x)=(x-10)(x+4)
So the domain of the function (g-f)(x) are the values for which the function exists. we can see that the function exists for all values of x.
Domain in set builder notation={x|x∈R}
Domain in interval notation=(-∞,∞)
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Solve for x.
-4≤16-4x
0 x <-5
Ο x <5
0 x > -5
Ο χ>5
The solution to the given inequality (-4 < 16 - 4x) is x < 5.
Hence, option B) x < 5 is the correct answer.
What is the solution to the given inequality?Given the in equality in the question;
-4 < 16 - 4x
First, rewrite the inequality such that x is on the left side.
-4x + 16 > -4
Subtract 16 from both sides
-4x + 16 - 16 > -4 - 16
-4x > -20
Divide both sides by -4
Note that when dividing both sides of an inequality by a negative value, the inequality sign flips direction.
-4x/-4 < -20/4
x < -20/-4
x < 5
The solution to the given inequality (-4 < 16 - 4x) is x < 5.
Hence, option B) x < 5 is the correct answer.
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How do I find out the check amount before the tip when the total amount was $55 with a 10% tip
Answer:$49.50
Step-by-step explanation:
First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.
simplify 14+(-8)+6+4+(-11)
Answer:
5
Step-by-step explanation:
PEMDAS
14-8+6+4-11
14-8=6
6+6=12
12+4=16
16-11=5
What is the simplest form ratio of 6oz flour, 4oz of sugar and 2 oz butter?
Answer:
3 : 2 : 1
Step-by-step explanation:
Simplest ratio
6oz : 4oz : 2 oz
Divide each by 2
6oz/2 : 4oz/2 : 2 oz/2
3 oz: 2 oz: 1 oz
3 : 2 : 1
What is the total cost of 2.3 cubic meters of soil if it sells for $45 per cubic meter?
The total cost is $
(Type an integer or a decimal.)
find the perimeter and area of the figure? G( -4,1), H(4,1),I(0,-2)
Perimeter = 18 units; Area = 9 sq. units
GH = √(-4-4)²+(1-1)² = 8 units
HI = √(4-0)²+(1+2)² = 5 units
IG = √(0+4)²+(-2-1)² = 5 units
Perimeter of the given triangle = 8+5+5=18 units
Semi-perimeter of triangle = 18÷2=9 units
Using Heron's formula; √[s(s-a)(s-b)(s-c)]=Area of triangle;
A= √(9)(9-8)(9-5)(9-5)
= √(9)(3)(3)
= 9 sq. units
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