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Answer:
10 and 24
Step-by-step explanation:
We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).
These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).
For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)
The side lengths are 10 and 24.
__
Check
For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.
__
In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...
x² +y² = (x+2)² ⇒ y² = (x² +4x +4) -x² ⇒ y² = 4x +4 = 4(x +1)
_____
Additional comment
The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.
Using the third equation in the attachment to write an expression for y, we have ...
y = 58 -2x
Substituting that into the second equation gives ...
(x(58 -2x)/2 = 120
29x -x² = 120
x² -29x +120 = 0
(x -5)(x -24) = 0 . . . . x = 5 or 24.
The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.
What is the following product?
(V12+ V6 (16-V10
6-12-2130+6-2V15
-2 དུ་
6V3-615
31/7- V22+2/3-4
2V3+6-2V15
Answer:
The answer is A: 6√2 - 2√30 + 6 - 2√15
Believe me it right.
Which of the SMART criteria are NOT met by this data analytics project goal (pay close attention to whether the options are words the SMART acronym stands for)?
Answer:
Specific
Step-by-step explanation:
The data analytics is defined as the study of analyzing the raw data and information so as to make a proper conclusion about the information. It is a process of inspecting, transforming, and modelling the data with the intention of finding useful information and conclusions.
The acronym for S.M.A..R.T is Specific, Measurable, Attainable, Relevant and Time bounding.
The SMAR criteria which do not meet the data analytics project goal in the question is "Specific".
A jewelry box is in the shape of a rectangular prism with an area of 528 cubic inches. The length of the box is 12 inches and the height is 5 1/2 inches. What is the width of the jewelry box? A=LxWxH
please help. :)
Which value of a in the exponential function below would cause the function to stretch?
f(x) = (1)
O 0.3
O 0.9
O 1.0
O 1.5
Answer:
1.5
Step-by-step explanation:
Took the test already.
The value of a for which the exponential function below would cause the function to stretch is a > 1 Or 1.5.
What are some rules for function transformations?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
We know an exponential function f(x) = [tex]e^x[/tex].
Now if we multiply f(x) by some number 'a' which is greater than 1 let it be g(x) = [tex]ae^x[/tex] the function would stretch horizontally for a > 1.
learn more about function transformations here :
https://brainly.com/question/13810353
#SPJ6
If three times a number added to 8 is divided by the number plus 7, the result is four thirds. Find the number.
9514 1404 393
Answer:
4/5
Step-by-step explanation:
The wording is ambiguous, as it often is when math expressions are described in English. We assume you intend ...
[tex]\dfrac{3n+8}{n+7}=\dfrac{4}{3}\\\\3(3n+8)=4(n+7)\qquad\text{multiply by $3(n+7)$}\\\\9n+24=4n+28\qquad\text{eliminate parentheses}\\\\5n=4\qquad\text{subtract $4n+24$}\\\\\boxed{n=\dfrac{4}{5}}\qquad\text{divide by 5}[/tex]
The number is 4/5.
The regression analysis can be summarized as follows: Multiple Choice No significant relationship exists between the variables. A significant negative relationship exists between the variables. For every unit increase in x, y decreases by 12.8094. A significant positive relationship exists between the variables
Answer:
A significant negative relationship exists between the variables
Step-by-step explanation:
Base on the information given in the question which goes thus : For every unit increase in x, y decreases by 12.8094. The value 12.8094 is the slope which is the rate of change in y variable per unit change in the independent variable. The sign or nature of the slope Coefficient gives an hint about the relationship between the x and y variables. The slope Coefficient in this case is negative and thus we'll have a negative relationship between the x and y variables (an increase in x leads to a corresponding decrease in y). This is a negative association.
Let f(x) = 5 + 12x − x^3. Find (a) the x- coordinate of all inflection points, (b)
the open intervals on which f is concave up, (c) the open intervals on which
f is concave down.
Answer:
A) x = 0.
B) f is concave up for (-∞, 0).
C) f is concave down for (0, ∞).
Step-by-step explanation:
We are given the function:
[tex]f(x)=5+12x-x^3[/tex]
A)
We want to find the x-coordinates of all inflection points.
Recall that inflections points (may) occur when the second derivative equals zero. Hence, find the second derivative. The first derivative is given by:
[tex]f'(x) = 12-3x^2[/tex]
And the second:
[tex]f''(x) = -6x[/tex]
Set the second derivative equal to zero:
[tex]0=-6x[/tex]
And solve for x. Hence:
[tex]x=0[/tex]
We must test the solution. In order for it to be an inflection point, the second derivative must change signs before and after. Testing x = -1:
[tex]f''(-1) = 6>0[/tex]
And testing x = 1:
[tex]f''(1) = -6<0[/tex]
Since the signs change for x = 0, x = 0 is indeed an inflection point.
B)
Recall that f is concave up when f''(x) is positive, and f is concave down when f''(x) is negative.
From the testing in Part A, we know that f''(x) is positive for all values less than zero. Hence, f is concave up for all values less than zero. Our interval is:
[tex](-\infty, 0)[/tex]
C)
From Part A, we know that f''(x) is negative for all values greater than zero. So, f is concave down for that interval:
[tex](0, \infty)[/tex]
Which is heavier, 4- kilograms
or
4
4 kilograms?
Answer:
i think 4 4 kilograms if im wrong sorry
Step-by-step explanation:
I need some help! thank you!
Answer:
The 1st,Thrid, Fifth Option
Step-by-step explanation:
The first option is true. We can move the orginal square root function to get g(x).
The second option is false. Function g(x) which equals
[tex] \sqrt{x - 3} - 1[/tex]
Domain is all real numbers greater than or equal to 3.
The third option is true. Since minimum point we can get is 0 in a square root function. We have a vertical shift so our new minimum point is
[tex]0 - 1 = - 1[/tex]
We can take the sqr root of 0 so
So all real numbers that are greater than or equal to -1 is true.
The fourth option is false, we need to add 3 instead of subtract 3.
The fifth option is true, we can do that to get back to our original function
identify the angles relationship
If he is correct, what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months
Complete Question
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 91 months with a standard deviation of 10 months if he is correct. what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad
Answer:
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Step-by-step explanation:
From the question we are told that:
Population mean \mu=91
Sample Mean \=x =2.08
Standard Deviation \sigma=10
Sample size n=68
Generally the Probability that The sample mean would differ from the population mean
P(|\=x-\mu|<2.08)
From Table
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
T Test
[tex]Z=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]Z=\frac{2.08}{\frac{10}{\sqrt{68} } }[/tex]
[tex]Z=1.72[/tex]
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
[tex]P(-1.72<Z<1.72)[/tex]
Therefore From Table
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Evaluate − x 2 −5 y 3 when x = 4 and y =−1
Answer:
-11
Step-by-step explanation:
I am going to assume that it is -x^2-5y^3.
-(4^2)-5(-1^3)
-16-5(-1)
-16+5
-11
Answer:
- 11
Step-by-step explanation:
If x = 4, y = -1
then,
- x^2 - 5y^3 = - (4)^2 - 5(-1)^3
= - 16 + 5
= - 11
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.
h = 7+23t-16t^2
Find all values of 1 for which the ball's height is 15 feet.
Answer:
Step-by-step explanation:
If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:
[tex]15=-16t^2+23t+7[/tex] and
[tex]0=-16t^2+23t-8[/tex]
Factor this however you factor a quadratic in class to get
t = .59 seconds and t = .85 seconds.
This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.
Use the functions below to complete Parts 1 and 2.
f(x)= |x| g(x)= |x+2| - 3
Part 1: Graph f(x) and g(x) on the grid below. Label each graph.
HINT: Making a table of values for each function may help you to graph them.
Part 2: describe how the graph of g(x) relates to the graph of its parent function, f(x).
HINT: Think about how f(x) was shifted to get g(x).
9514 1404 393
Answer:
1. see below
2. g(x) is f(x) translated left 2 and down 3
Step-by-step explanation:
1. The graphs are attached. F(x) is in red; g(x) is in blue.
__
2. The graph of g(x) = f(x -h) +k is the parent function translated by (h, k). Here we have (h, k) = (-2, -3), so g(x) is f(x) translated left 2 and down 3.
Suppose f(x)=x^2. What is the graph of g(x)=1/2f(x)?
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).
The graph of g(x) is attached.
What is the solution to this equation?
6
O A. x = 18
O B. x= -2
O c. x= -18
O D. X= 21
−3 1/2 ÷ 1 1/4
khan academy
answer in simplified proper fraction
or
simplified improper fraction
Answer:
Step-by-step explanation:
Change the mixed numbers to improper fractions.
Umm.. Hi there! Can someone please help me out with this? (only for those who know the answer)
Bcoz I really need this rn :(
DUEEEE AFTERRR LUNCHH! :(:(:(:(
If your answer is NONSENSE it will be deleted as soon as possible!
But if your answer is CORRECT, HELPFUL, HAS AN EXPLANATION, I'll chose your answer as the BRAINLIEST ANSWER!
Answer:
The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.
The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2
Explanation:
Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.
The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.
I hope this helps!
Answer:
In LDR
Exterior = d Interior = a, bIn PDR
Exterior = 4Interior = 1, 2Exterior angle of a triangle is formed when one side of the triangle is extended .
Interior remote angles the angles in the triangle that do not lie on the extended side.
Simplify 3/4 + 5/8 over 3/4 - 1/2
Answer:
11/2
Step-by-step explanation:
[tex]\frac{\frac{3}{4} + \frac{5}{8} }{\frac{3}{4} - \frac{1}{2} }[/tex]
= 3/4 + 5/8 = 11/8 (take LCM)
3/4 - 1/2 = 1/4 (take LCM)
11/8 ÷ 1 /4
= 11/8 x 4
= 11/2
Answered by Gauthmath
I need help finding the answer to this question on edge.
Answer:
6
Step-by-step explanation:
We need to evaluate :-
[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]
Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,
[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]
Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,
[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]
Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,
[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]
Hence the required answer is 6.
find c.round to the nearest tenth
Answer:
we need a picture...
Step-by-step explanation:
. Mildred bought an old
necklace and pair of earrings
while at an antique show. If
the cost of the jewelry is ]
and tax is 7%, which of the
following equations could be
used to find the total cost of
the jewelry?
a. .07 + ]
b. J +.07 x)
C. (.07x)) + ]
d. 7) + ]
Answer:
j * .07 +j
Step-by-step explanation:
The tax on the jewelry is J* .07
Add the tax to the cost of the jewelry to get the total cost
j * .07 +j
g Find an equation of the line with slope m that passes through the given point. Put the answer in slope-intercept form. (-4, 8), undefined slope Hint: Any line parallel to Y axis has undefined slope.
Answer:
The equation is x + 4 = 0.
Step-by-step explanation:
Point (-4 , 8)
A line parallel to the Y axis has slope is infinite.
The equation of line is
[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]
An oil tanker spills oil that spreads in a circular pattern whose radius increases at a rate of 15 ft/min. Let A be the area of the circle and r be the radius of the circle. How fast is the area increasing when the radius is 30 feet
Answer:
[tex]2827.4 \dfrac{ft}{s}[/tex]
Step-by-step explanation:
[tex] A = \pi r^2 [/tex]
[tex] \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt} [/tex]
[tex] \dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s} [/tex]
[tex] \dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s} [/tex]
need assistance with this, thank you
Answer:
B. 1✓3 in.
Search It ok
I see the answer :)
Solve for x.
7(x+2) = 6(x+5)
O x=-44
O X=-16
O x= 44
O x= 16
Answer:
x = 16
Step-by-step explanation:
7(x + 2) = 6(x + 5)
First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.
7x + 14 = 6x + 30
Next, let's subtract "6x" from both sides of this equation!
x + 14 = 30
Now, we have to subtract "14" from both sides of the equation.
x = 16
Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.
7(16 + 2) = 6(16 + 5)
7(18) = 6(21)
126 = 126
Since our equations equal each other we know that our x-value is correct!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Find the slope and then an equation for each line.
Which of these shapes have the same area?
Answer:
wheres the picture?
Step-by-step explanation:
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
9514 1404 393
Answer:
3
Step-by-step explanation:
The length of A'B' is 3 units.
The length of AB is 1 unit.
The scale factor is A'B'/AB = 3/1 = 3.
help me with my work pls
Answer:
-75/4
Step-by-step explanation:
75 x 100 = 7500
4 x 100 = 400
