Answer:
see below
Step-by-step explanation:
fx=x^2+2x+3
This is a parabola that opens upward
f(x) = (x^2 +2x)+3
= (x^2+2x+1) +3-1
= (x+1)^2 +2
This is in vertex form y =a(x-h)^2 +h where the vertex is (h,k)
This has a vertex as (-1,2)
And has a y intercept at (0,3)
this does not cross the x axis
The average salary for a certain profession is $87,500. assume that the standard deviation of such salaries is $26,000. Consider a random sample of 63 people in this profession and let xbar represent the mean salary for the sample.a. What is ?
b. What is ?c. Describe the shape of the sampling distributio of ?
d. Find the z-score for the value =80,000.
e. Find P( > 80,000).
Solution :
Given data:
Mean, μ = $87,500
Standard deviation, σ = $26,000
Sample number, n = 63
a). The value of [tex]$\mu_{x}$[/tex] :
[tex]$\mu_x=\mu$[/tex]
= 87,500
b). The value of [tex]$\sigma_x$[/tex] :
[tex]$\sigma_x = \frac{\sigma}{\sqrt n}$[/tex]
[tex]$\sigma_x = \frac{26000}{\sqrt {63}}$[/tex]
= 3275.69
c). The shape of the sampling distribution is that of a normal distribution (bell curve).
d). The value z-score for the value =80,000.
[tex]$z-\text{score} =\frac{\overline x - \mu}{\sigma - \sqrt{n}}$[/tex]
[tex]$z-\text{score} =\frac{80000-87500}{26000 - \sqrt{63}}$[/tex]
= -2.2896
≈ -2.29
e). P(x > 80000) = P(z > -2.2896)
= 0.9890
Find all points of intersection of the given curves. (Assume 0
blank.)
R= 1 - cos(Theta), r = 1 + sin(theta)
9514 1404 393
Answer:
POLE(1+(√2)/2, 3π/4)(1-(√2)/2, 7π/4)Step-by-step explanation:
Your have correctly identified the points of intersection, but you need to follow directions in your entry of those answers. "POLE" goes in the first answer slot. You may also be expected to rationalize the denominator, or provide the r value as a single term.
The points of intersection are ...
POLE
((2+√2)/2, 3π/4)
((2-√2)/2, 7π/4)
Which of the following is equal to -16?
Answer:
The last one. 4.
Step-by-step explanation:
The square root of a positive or negative number can't be negative. so it's positive 4.
If x2-y2 = 10 and x+y = 5, what is the value of x-y? 2-5?
Answer:
x-y=2
I don't get why they are asking you what is 2-5. That seems super basic compared to the other question it is with. Since 5-2=3, then 2-5 or -5+2=-3.
Step-by-step explanation:
We are going to use identity x^2-y^2=(x-y)(x+y)
x^2-y^2=10
(x-y)(x+y)=10
(x-y)(5)=10
Since (2)(5)=10, this implies x-y=2.
I need the answer to this
Answer:
[tex]A)\:x<12[/tex]
[tex]5(x+5)<85\\5x+25<85\\5x<85-25\\5x<60\\x<12[/tex]
OAmalOHopeO
Answer:
x < 12.................................
The sum of 3 unequal odd numbers is 203. What may those numbers be? Give four possible answers.
Answer:
71, 69 and 63
71, 67 and 65
73, 67 and 63
75, 65 and 63
Express the set shown below in roster form. {x | x is a natural number less than -2}
Given:
The set is:
[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]
To find:
The raster form of the given set.
Solution:
We know that, natural numbers are all positive integers.
Natural numbers: 1, 2, 3, 4,... .
The given set is:
[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]
Here, x is a natural number and it is less than -2, which is not possible.
Since all natural numbers are greater than or equal to 1, therefore the given set has no element.
[tex]\{x|x\text{ is a natural number less than }-2=\phi[/tex]
Therefore, the roaster form of the given set is [tex]\phi[/tex] or [tex]\{\ \}[/tex].
A cone has a radius of 5 ft and a height of 15 ft. It is empty and is being filled with water at a constant rate of 24 ft 3 / sec . Find the rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 ft. (You must also include the units)
Answer:
The rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 feet is approximately 0.637 feet per second.
Step-by-step explanation:
The volume of the cone ([tex]V[/tex]), in cubic feet, is defined by the following equation:
[tex]V = \frac{\pi}{3}\cdot r^{2}\cdot h[/tex] (1)
Where:
[tex]r[/tex] - Radius, in feet.
[tex]h[/tex] - Height, in feet.
And there is the following ratio of the radius to the height is:
[tex]\frac{r}{h} = k[/tex] (2)
By applying (2) in (1):
[tex]h = \frac{r}{k}[/tex]
[tex]V = \frac{\pi}{3\cdot k}\cdot r^{3}[/tex] (3)
And the rate of change of the radius is found by differentiating on (3):
[tex]\dot V = \frac{\pi}{k}\cdot r^{2}\cdot \dot r[/tex] (4)
Where:
[tex]\dot V[/tex] - Rate of change of the volume, in cubic feet per second.
[tex]\dot r[/tex] - Rate of change of the surface of the water, in feet per second.
[tex]\dot r = \frac{k\cdot \dot V}{\pi\cdot r^{2}}[/tex]
If we know that [tex]k = \frac{1}{3}[/tex], [tex]\dot V = 24\,\frac{ft^{3}}{s}[/tex] and [tex]r = 2\,ft[/tex], then the rate of change of the radius of the surface of the water is:
[tex]\dot r = \frac{\left(\frac{1}{3} \right)\cdot \left(24\,\frac{ft^{3}}{s} \right)}{\pi\cdot (2\,ft)^{2}}[/tex]
[tex]\dot r = 0.637\,\frac{ft}{s}[/tex]
The rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 feet is approximately 0.637 feet per second.
❤❤❤❤❤❤I WILL MARK AS BRAINLIEST IF RIGHT PLEASE HELP ME PLEASE BE CORRECT BEFORE ANSWERING PLEASE AND THANK YOU.
TELL ME WHERE TO PUT EACH POINT OF THE TRIANGLE TY
Answer:
Please look at the picture
Step-by-step explanation:
Please look at the picture I have drawn it for you
Solve 60 ÷ 5(1 + 1(1 + 1))
Answer:
Creo que es 36
Step-by-step explanation
:D
Answer:
36
Step-by-step explanation:
Lisa made a shirt using 1/3 m of blue fabric and 3/5 m of red fabric how many meters of fabric did she use in all
Answer: 14/15 of a meter
Step-by-step explanation:
5 and 3 LCM is 15.
3/5 x 3 + 1/3 x 5= 9/15 + 5/ 15 = 14/15
solve by completing the square method 3x²=15-4x
Answer:
Step-by-step explanation:
3x²=15-4x
divide by 3 on both sides
x²=5-[tex]\frac{4}{3}[/tex]x
move everything to one side
x²+[tex]\frac{4}{3}[/tex]x -5 = 0
add the square of 1/2 the middle term of [tex]\frac{4}{3}[/tex] but also subtract it too
x²+[tex]\frac{4}{3}[/tex]x +[tex]( \frac{2}{3} )^{2}[/tex]-5-[tex]( \frac{2}{3} )^{2}[/tex] = 0
now use the property of a perfect square to rewrite
[tex](x+\frac{2}{3}) ^{2}[/tex] -5 -[tex]\frac{4}{9}[/tex] = 0
rewrite 5 as a fraction
[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{45}{9}[/tex]- [tex]\frac{4}{9}[/tex] = 0
add up the fractions
[tex](x+\frac{2}{3}) ^{2}[/tex] - [tex]\frac{49}{9}[/tex] = 0
move to the other side
[tex](x+\frac{2}{3}) ^{2}[/tex] = [tex]\frac{49}{9}[/tex]
take the square root of both sides :P
[tex]\sqrt{((x+\frac{2}{3}) ^{2} }[/tex] = [tex]\sqrt{\frac{49}{9} }[/tex]
much easier looking now, just use algebra to solve for x
x + [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]
subtract [tex]\frac{2}{3}[/tex] from both sides
x + [tex]\frac{2}{3}[/tex] - [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex] - [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{3}[/tex]
:)
Answer:
x = - 3, x = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Given
3x² =15 - 4x ( add 4x to both sides )
3x² + 4x = 15 ← factor out 3 from each term on the left side
3(x² + [tex]\frac{4}{3}[/tex] x) = 15
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + [tex]\frac{4}{3}[/tex] x
3(x² + 2([tex]\frac{2}{3}[/tex] )x + [tex]\frac{4}{9}[/tex] - [tex]\frac{4}{9}[/tex] ) = 15
3(x + [tex]\frac{2}{3}[/tex] )² - [tex]\frac{4}{3}[/tex] = 15 ( add [tex]\frac{4}{3}[/tex] to both sides )
3(x + [tex]\frac{2}{3}[/tex] )² = 15 + [tex]\frac{4}{3}[/tex] = [tex]\frac{49}{3}[/tex] ( divide both sides by 3 )
(x + [tex]\frac{2}{3}[/tex] )² = [tex]\frac{49}{9}[/tex] ( take the square root of both sides )
x + [tex]\frac{2}{3}[/tex] = ± [tex]\sqrt{\frac{49}{9} }[/tex] = ± [tex]\frac{7}{3}[/tex] ( subtract [tex]\frac{2}{3}[/tex] from both sides )
x = - [tex]\frac{2}{3}[/tex] ± [tex]\frac{7}{3}[/tex], then
x = - [tex]\frac{2}{3}[/tex] - [tex]\frac{7}{3}[/tex] = - 3
x = - [tex]\frac{2}{3}[/tex] + [tex]\frac{7}{3}[/tex] = [tex]\frac{5}{3}[/tex]
please help
find 0.
Answer:
0=70!!!!!!!!!!!!!!!!!!!!!!
prove that: cos^2 (45+A)+cos^2 (45-A)=1
Answer:
see explanation
Step-by-step explanation:
Using the cosine addition formula
cos(A ± B ) = cosAcosB ∓ sinAsinB
Then considering the left side
cos²(45 + A) + cos²(45 - A)
= [ cos45cosA - sin45sinA ]² + [cos45cosA + sin45sinA]]²
= [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA - [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]² + [ [tex]\frac{1}{\sqrt{2} }[/tex] cosA + [tex]\frac{1}{\sqrt{2} }[/tex] sinA ]²
= [tex]\frac{1}{2}[/tex]cos²A - sinAcosA + [tex]\frac{1}{2}[/tex] sin²A + [tex]\frac{1}{2}[/tex] cos²A + sinAcosA + [tex]\frac{1}{2}[/tex] sin²A
= cos²A + sin²A
= 1
= right side , then proven
Answer:
Step-by-step explanation:
cos 2x=cos²x-sin²x=cos²x-(1-cos²x)=cos²x-1+cos²x=2cos²x-1
2cos²x=1+cos2x
[tex]cos^2x=\frac{1}{2}(1+cos2x)[/tex]
cos²(45+A)+cos²(45-A)
[tex]=\frac{1}{2}(1+cos(90+2A))+\frac{1}{2}(1+cos(90-2A))\\=\frac{1}{2} (1-sin2A)+\frac{1}{2} (1+sin 2A)\\=\frac{1}{2} (1-sin2A+1+sin 2A)\\=\frac{1}{2} \times2\\=1[/tex]
cos (90-x)=sin x
cos (90+x)=-sin x
3 hundreds equal how many tens
Answer:
There are 30 tens in 3 hundred.
Step-by-step explanation:
there are thirty tens in 3 hundred
Find the lateral area of this square based pyramid. 10in 5in (in the image)
Answer:
100 in²
Step-by-step explanation:
4 triangles, each of them has area = 10*5/2
so total area = (10*5/2)*4
= (10*5*2)
= 100 in²
Answered by GAUTHMATH
The lateral surface area of the pyramid is 100 in²
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.
4 triangles, each of them has an area = 10 x ( 5/2 )
So total area = (10 x 5/2) x 4
Total area = (10 x 5 x 2)
Total area = 100 in²
Therefore the lateral surface area of the pyramid is 100 in²
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3) Consider the sequence -11 ; 2sin3x ; 15; ...
3.1.1) Determine the values of x in the interval [0 ; 90] for whichthe sequence will be arithmetic.
Write the quadratic equation in standard form:
7x + 8 + 2x2
2x + 1 + x2
Answer:
[tex]3x^2 + 9x +9[/tex]
Step-by-step explanation:
Given
[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]
Required
The result in standard form
We have:
[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]
Remove brackets
[tex]7x + 8 + 2x^2 + 2x + 1 + x^2[/tex]
Collect like terms
[tex]7x+ 2x + 8 + 1 + 2x^2+ x^2[/tex]
[tex]9x + 9+ 3x^2[/tex]
The standard form of a quadratic equation is:
[tex]ax^2 + bx + c[/tex]
So, we have:
[tex]9x + 9+ 3x^2[/tex]
[tex]3x^2 + 9x +9[/tex]
45 points! Hello! The area of a rectangular pool is given by the trinomial 4y2 + 6y – 10. What are the possible dimensions of the pool? Use factoring.
Thank you to however helps me!
Answer:
The dimensions are (2y+5) by 2(y-1) or 2(2y+5) by (y-1)
Step-by-step explanation:
4y^2 + 6y – 10
Factor the expression
Factor out the greatest common factor
2 ( 2y^2 +3y -5)
2 ( 2y+5) ( y-1)
A = l*w
The dimensions are (2y+5) by 2(y-1) or 2(2y+5) by (y-1)
use the figure to find y
Answer:
y = 3
Step-by-step explanation:
6sin(30) = 3
-3u-17=(u+8)
simplify
Answer:
-25/4 = u
Step-by-step explanation:
-3u-17=(u+8)
Add 3u to each side
-3u+3u-17=(u+3u+8)
-17 = 4u +8
Subtract 8 from each side
-17-8 = 4u+8-8
-25 = 4u
Divide by 4
-25/4 = 4u/4
-25/4 = u
You are walking from home to a grocery store you stop for a rest after 2/5 miles the grocery store is actually 3/4 miles from home how much farther do you have to walk
Answer:
7/20 mile farther
Step-by-step explanation:
Subtracting 2/5 mile from 3/4 mile results in the distance you still have to walk:
3/4 - 2/5 = ?
Here the LCD is 20. Thus, 3/4 becomes 15/20 and 2/5 becomes 8/20.
Then 3/4 - 2/5 = 15/20 - 8/20, or 7/20.
You still have 7/20 mile to walk to get home.
HJ= 5x -3, JK= 8x -9 and KH= 131
Answer:
HJ = 52
JK = 79
Step-by-step explanation:
Hello, I want to assume you are trying to determine either HJ or JK. Below is an illustration of how to determine either HJ or JK.
From the question given above, the following data were obtained:
HJ = 5x – 3
JK = 8x – 9
KH = 131
If we draw a straight line, we'll observe the following:
H_______J_______K
KH = HJ + JK
Next, we shall determine the value of x.
HJ = 5x – 3
JK = 8x – 9
KH = 131
KH = HJ + JK
131 = (5x – 3) + (8x – 9)
131 = 5x – 3 + 8x – 9
Collect like terms
131 + 3 + 9 = 5x + 8x
143 = 13x
Divide both side by 13
x = 143 / 13
x = 11
Finally, we shall determine HJ and JK. This can be obtained as follow:
For HJ:
HJ = 5x – 3
x = 11
HJ = 5(11) – 3
HJ = 55 – 3
HJ = 52
For JK:
JK = 8x – 9
x = 11
JK = 8x – 9
JK = 8(11) – 9
JK = 88 – 9
JK = 79
Select the correct answer.
Each statement describes a transformation of the graph of y=x. Which statement correctly describes the graph of y= x - 13?
OA. It is the graph of y= x translated 13 units to the right.
OB. It is the graph of y=xwhere the slope is decreased by 13.
It is the graph of y= x translated 13 units to the left.
OD. It is the graph of y= x translated 13 units up.
ОС.
minus sign ironically makes it go to the right
because the function crosses the y axis at -13
It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of transformation, we have to compare the two equations and look for changes.
In the equation y = x - 13, we subtract 13 from the value of x.
This means that the graph of y = x is shifted 13 units downwards,
since every point on the graph has 13 subtracted from its y-coordinate.
Hence, It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
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Eddie is using his phone's calculator app to calculate 16,544 × 70. He accidentally enters 16,544 × 7 instead. How can he correct his mistake
Answer:
Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.
Subtract the second equation from the first.
8x + 3y = 14
(4x + 3y = 8)
-
O A. 6y = 22
O B. 4x = 6
O c. -6y = 6
D. 12x = 22
Please help
Answer:
B
Step-by-step explanation:
Subtracting second equation from first, term by term , gives
(8x - 4x) + (3y - 3y) = (14 - 8) , that is
4x + 0 = 6, so
4x = 6 → B
work out the equasion 39+(−13)
Answer:
39-13=26
Step-by-step explanation:
plus(minus)=minus
What are the solutions to the equation
Answer:
(0,1) and (3,4)
Step-by-step explanation:
It's the points where they meets, judging the graph, it's x = 0, y = 1 and x = 3, y = 4
put them in the equation and you'll see the the values satisfies the equation
Answered by GAUTHMATH
The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters
Answer:
Given E(t)=1100(100-t)+580(100-t)^2
Put t = 99.5, we get
E(99.5)=1100(100-99.5)+580(100-99.5)^2
E(99.5)=1100(0.5)+580(0.5)^2
E(99.5)=1100(0.5)+580(0.25)
E(99.5)=550+145
E(99.5)=695m
Step-by-step explanation:
It can be concluded that -
E(99.5) = 695
E(100) = 0
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the function as follows -
E(t) = 1100(100 - t) + 580(100 - t)²
The given function is -
E(t) = 1100(100 - t) + 580(100 - t)²
At → E(99.5)
E(99.5) = 1100(100 - t) + 580(100 - t)²
E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²
E(99.5) = 1100(0.5) + 580(0.5)²
E(99.5) = 550 + 145
E(99.5) = 695
At → E(100)
E(100) = 1100(100 - t) + 580(100 - t)²
E(100) = 1100(100 - 100) + 580(100 - 100)²
E(100) = 0
Therefore, it can be concluded that -
E(99.5) = 695
E(100) = 0
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The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.
The restricted domain for ƒ is ?
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
