Answer:
(-1.5,0)
Step-by-step explanation:
Find the average for the x and y values.
x = [tex]\frac{(-5+ 2)}{2}[/tex] = [tex]\frac{-3}{2}[/tex] or -1.5
y = [tex]\frac{(5- 5)}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
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
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].
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.)
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
To learn more about number of big boxes visit :
https://brainly.com/question/14041970
#SPJ9
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
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
To learn more about this; visit: https://brainly.com/question/24701453
#SPJ9
x^3-9x^2-4x+36=0
Determine the values of x for which the function f(x)= x^2-5x-2/ 5x-3
A. is zero
B. is positive, and
C. is negative
Answer:
B
Step-by-step explanation:
use the formula x = [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]x= \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
according to the known condition, a = 1, b = -5-2/5 c = -3
you can input these values into the above two.
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 unit digits of 3^40
Answer:
1
Step-by-step explanation:
the answer is 1.21576655000000000.
the unit of this no. is 1.
DES
Question: 2/20
Find the next number in the sequence: 1, 1, 2, -1, 1, -2, -1,
Eigenvalues are the special set of scalar values that is associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed as characteristic roots. It is a non-zero vector that can be changed at most by its scalar factor after the application of linear transformations.
0 Eigenvalue
3 Eigenvalue
The y values of any nxn matrix A that adhere to the following criteria are considered to be its eigenvalues.
When I is the order n identity matrix, det(A - yI) = 0.
In this case, A = [1 2; 1 2], I = [1 0; 0 1], and yI = [y 0; 0 y]. I've added a new line in this notation with ;.
A - yI = [1-y 2; 1 2-y]
det(A - yI) = 1 - y* In other words, - 2 = = 2 - y - 2y + y2 - 2 = 0 = y2 - 3y = 0 = y(y-3) = 0.
y = 0 or y - 3 = 0
y = 3
To learn more about Eigenvalues Visit : https://brainly.com/question/13144436
#SPJ9
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
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:
17.
Peter transports metal bars in his van.
The van has a safety notice: "Maximum Load 1200 kg".
Each metal bar has a label: "Weight 60 kg".
For safety reasons, Peter assumes that:
1200 is rounded correct to 2 significant figures, and
60 is rounded correct to 1 significant figure.
Calculate the greatest number of bars that Peter can safely put into the van if his assumptions are
correct.
Answer:
17 bars
Step-by-step explanation:
Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.
Range of valuesThe error in a rounded number is assumed to be as much as half of the least significant digit of the number.
Peter's load limit may actually be as low as ...
1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100
Peter's bar weight might be as high as ...
60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10
Safe loadingIf Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...
(1150 kg) / (65 kg/bar) ≈ 17.7 bars
The greatest number of bars Peter can load safely is 17.
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.
Bob is x years old. His brother, Matt, is 4 years older than Bob. Their aunt, Lana, is 5 years less than twice Matt’s age.
Write and simplify an expression that represents Lana’s age in years.
Answer:
9 9 years 9999999999999
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
[tex]-6y + 4 = | 4y + 12 |[/tex]
Answer: its not equal.
Step-by-step explanation:
-6y + 4 = 2 (-3y + 2)
|4y + 12| = 4 (y + 3)
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.
To learn more about functions:
https://brainly.com/question/12431044
#SPJ9
Evaluate the expression when m= -4
m2 +6m +9
Answer: 36. Substitute: - 32 - 6 * - 3 + 9 Remove the parentheses: 32 + 6 * 3 + 9 Calculate the power:9 + 6 * 3 + 9.
Step-by-step explanation: I hope this help
Answer:
= 1
Step-by-step explanation:
m² + 6m + 9
m = -4
= -4² + 6*-4 + 9
= 16 -24 + 9
= 25 - 24
= 1
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.
Learn more about angle here
https://brainly.com/question/1592456
#SPJ9
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=(-∞,∞)
To learn more about domain and range:
https://brainly.com/question/28135761
#SPJ9
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.
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.
Learn more about inequality here: brainly.com/question/20296065
#SPJ1
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
You are choosing between two health clubs. Club A offers membership for a fee of plus $18 a monthly fee of $20 Club B offers membership for a fee of $12 plus a monthly fee of $23 After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Please help thank you
Answer:
x=5
Step-by-step explanation:
so after five months, the costs would equal each other.
Explanation:
You'd have to write equations for the price per month for each club.
Let x equal the number of months of membership, and y equal the total cost. Club A's is y=25x+40 and Club B's is y=30x+15.
Because we know that the prices, y, would be equal, we can set the two equations equal to each other.
25x+40=30x+15.
We can now solve for x by isolating the variable.
25x+25=30x.
25=5x.
5=x
After five months, the total cost would be the same.
-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.
More can be learned about inequalities at https://brainly.com/question/25235995
#SPJ1
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
learn more about perimeter here:
https://brainly.com/question/28499208
#SPJ9
If you have only $50, can you afford to buy a pair of shoes marked $69.99?
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
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.