[tex]\textsf {21 cm}[/tex]
[tex]\textsf {If it is correct to the nearest centimeter, then the least side length}\\\textsf {would be 8 - 1 = 7 cm. }[/tex]
[tex]\textsf {Then, the least possible perimeter would be :}[/tex]
[tex]\mathsf {7 \times 3}[/tex]
[tex]\textsf {21 cm}[/tex]
the perimeter of a right angle triangle is 24 cm and its area is 24 cm square if the hypotenuse is 13 cm find the remaining sides
Answer:
let the remaining sides be X and Y
perimeter = X + Y + 13
24 = X + Y + 13
11 = X + Y ---(1).
Area = 1/2 * base * height
24 = 1/2 * X * Y
XY = 48.-----(2)
solving eq 1 and 2
X + Y = 11
XY = 48
Xy + y² = 11y
Xy = 48
y²= 11y - 48
y² -11y + 48 = 0
no real solution of this equation.
Answer:
Step-by-step explanation:
the triangle is NOT a 3–4–5 or multiple,
so it is not a right triangle or your data is wrong.
marcus needs to paint a large wall with a window centered in the middle of the wall (shown below).what is the area (in square feet)that marcus will need to paint.
A 336ft
B 256ft
C 300ft
D 264ft
To calculate the area that Marcus needs to paint we must calculate the area of the window and subtract it from the total area of the wall.
How to calculate the area of a wall?To calculate the area of a rectangular wall we must use the following formula:
area = a × bWhere a is the length of the height, and b is the length of the width.
Next, we need to calculate the area of the window. If it is a square or rectangular window we use the same formula "area = a × b".
If the window is circular we use this formula:
Area of the circle = π r²Once we know the area of the wall and the area of the window, we subtract the area of the window from the area of the wall and we will know what is the total area that Marcus must paint.
Note: This question is incomplete because some information is missing. However I can answer it based on my general prior knowledge.
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If $5x-7=13x+17$, what is $6(x-4)$?
Answer:
0(x-4)
Step-by-step explanation:
in my working system i mean just when i try on the place of 4 any number can be inserted
$5x-7=13x+17$,here both gives -22 as a result so
$6(x-4)$=6x-24 and to give the same result or 0
$6(x-4)$=0(x-any number )
What function represents this graph??
The required piecewise function that represents the graph is given as:
[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]
Piecewise functionsThe graph consists of 3 lines with different equations and slopes. In order to determine the function it represents, we will create a piecewise function.
For the line crossing the negative x-axis
Using the coordinate points (-4, 2) and (-2, -4)
Slope = -6/2
Slope = -3
2 = -3(-4) + b
2 - 12 = b
b = -10
The equation of the line will be y = -3x-10
For the line crossing the negative y-axis
Using the coordinate points (-2, -4) and (2,-2)
Slope = 2/4
Slope = 1/2
-2 = 1/2(2) + b
-2 - 1 = b
b = -3
The equation of the line will be y = -1/2x-3
For the line crossing the positive x-axis
Using the coordinate points (2, -2) and (3, 0)
Slope = 2/1
Slope = 2
0 = 2(3) + b
0 - 6 = b
b = -6
The equation of the line will be y = 2x-6
The required piecewise function that represents the graph is given as:
[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]
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Expand & simplify 6 ( p + 6 ) + 2 ( p + 4 )
Solution: 8p+44
Detailed explanation:
First we can "expand" by multiplying 6 times the parentheses and then 2 times the other set of parentheses.
[tex]--\mapsto\boldsymbol{6(p+6)+2(p+4)}\\\\---\mapsto\boldsymbol{6p+36+2p+8}[/tex]
To make life easier let's just put the p's next to each other.
[tex]--\mapsto\boldsymbol{6p+2p+36+8}[/tex]
Now let's add the p's
[tex]---\mapsto\boldsymbol{8p+44}[/tex]
Voila! There's our answer!
Cheers! ^-^__________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
____________________
⚜What are the domain and range of the function represented by the set of
ordered pairs?
{(-7, 1), (-3, 2), (0, -2), (5,5)}
Answer:
see explanation
Step-by-step explanation:
the domain is the set of x- coordinates from the ordered pairs , that is
domain : { - 7, - 3, 0, 5 }
the range is the set of y- coordinates from the ordered pairs, that is
range : { - 2, 1, 2, 5 }
x=y²-1
2x - y = 4
Which of the following equations could be the result of using substitution to solve the system?
2y²-y-5=0
2y2-y-6=0
2y2-2y-5=0
Answer:
B) 2y² - y - 6 = 0
Given following:
x = y² - 1 ___equation 12x - y = 4 ___equation 2Insert equation 1 into 2:
2(y² - 1) - y = 42y² - 2 - y = 42y² - y - 2 - 4 = 02y² - y - 6 = 0Put in second
2x-y=42(y²-1)-y=42y²-2-y=42y²-y-6=0Find the range of the given function y = 8x + 1, where x > 2.
The range of the function will be all values that are greater than 17 that is y > 17
Range of a functionThe range of a function is the dependent variable of the function for which it exists,
Given the linear function
y = 8x + 1
If the value of x is 2, hence;
y = 8(2) + 1
y = 17
Hence the range of the function will be all values that are greater than 17 that is y > 17
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Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
The direct distance from A to C is more than yards.
The direct distance form A to C is represented by the inequality
AC < 40 yards.
What is a Triangle ?A triangle is a polygon with three sides , three vertices and three angles.
It is given that
Distance form point A to B is 15 yards
Distance form point B to C is 25 yards.
Distance AC = ?
In a Triangle the sum of two sides is always greater than the third side.
Therefore
AC < 15 +25
AC < 40 yards.
Therefore the direct distance form A to C is represented by the inequality AC < 40 yards.
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Find the value of :
[tex] \sf log_{3 \sqrt{2} }(324) [/tex]
Answer:
4
Step-by-step explanation:
Is that a log with the base of 3√(2) ?
If so....my calculator says the answer is 4
Let's see if we can do it w/ou the calculator:
3 sqrt(2)^x = 324 = 3^4 * 2^2 Now 'LOG' both sides:
x log (3 sqrt 2) = log (3^4 *2^2) = 4 log ( 3 * 2^(2/4)) = 4 log (3 sqrt2)
now divide both sides by log (3 sqrt2 )
x = 4 (If I did the math correctly ! )
I finished all my other questions but i don't know how to do this one. could someone help me? I added 100 points. It is attached. :)
The answers are mentioned below.
What is Acceleration ?Acceleration is the change of speed with respect to time.
It is given that ,
The mass of the person is 50kg
Weight is 490 N
He has boarded an elevator with a bathroom scale.
1. The elevator is going down at constant speed , Force = 0N as acceleration is zero , The reading is 50kg.
2. The elevator is going up an slowing down . The magnitude of the acceleration is 4.9 m/sq.s , Force = mass * acceleration = 50 * 4.9 = 245N acting upward but the net force will be acting downward.
490 - 245 = 145N , reading 14.79 kg.
3.The elevator is free falling with an acceleration of 9.8m/sq.s force 0 N , as the gravitational force is pulling you down and the scale pushes up with the same force , Reading is 0 kg.
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If three standard six-sided die were rolled with the numbers showing on each recorded, how many equally likely outcomes would be in the sample space?
Answer:
216
Step-by-step explanation:
You are rolling three die three times
a die has six sides
to obtain the sample space
we would have to multiply 6 x 6 x 6
which could account for the three roles which would be equivalent to the sample space
6^3
If you apply the changes below to the quadratic parent function, f(x) = x²,
which of these is the equation of the new function? Shift 1 unit left.
Vertically stretch by a factor of 5.
Reflect over the x-axis.
A. g(x) = -5(x-1)²
B. g(x) = -5x² - 1
C. g(x) = -5(x + 1)²
D. g(x) = (-5x + 1)²
Answer:
Step-by-step explanation:
Comment
Do the most mechanical part first. Moving 1 unit left will mean that x becomes (x + 1). It is anti intuative, but that is the correct answer.
So far what you have is y = a(x + 1)^2
The reason that you want to do it this way is any answer with a minus sign is wrong which eliminates A and B
When you stretch the parabola, a becomes 5 so now you have another part of the puzzle. and the equation becomes
y = 5(x + 1)^2
The 5 goes on the outside of the brackets which eliminates D
When you reflect this over the x axis, you invert the parabola which means you turn it upside down. The sign in front of the 5 becomes a minus.
Answer
y = - 5(x + 1)^2 or C.
Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.
{(-3, 7.5) , (-2, 10) , (-1, 12.5)}
Write the equation of the graph for the set of ordered pairs.
{(1, 150) , (2, 112.5) , (3, 84.375)}
Write the equation of the graph for the set of ordered pairs.
Find the slope of the line whose equation is 3x - 4y = 7.
Answer:
0.75
Step-by-step explanation:
slope is the coeffecient of x when the equation is in the order yb= mx + b
3x - 4y = 7
-4y = 7 - 3x
4y = 3x - 7
y = (3x - 7) / 4
y = 3x / 4 - 7 / 4
slope = 3/4
Please helpppp !!!!!
Answer:
The answer is A
Identify the domain of the given function.
Answer:
choice C
Step-by-step explanation:
x could be any number except -1.
Cause for x=-1 the denominator becomes undefined.
21 added to a number is the same as 37
Answer:
Step-by-step explanation:
Hi, let me help you out.
First I'm going to turn the verbal phrase into an algebraic phrase...
21+n=37. here n is the unknown number
Next, I believe you need to find what n equals.
This can be done by subtracting 21 from both sides.
n=37-21
n=16
Thus the number we need is 16.
_________________
Hope I helped. Best wishes.
How would you describe the graph of y< - lxl?
A dashed line up V on the (0,0) with the shading on the inside of the V.
A solid line up V on the (0,0) with shading outside the V.
A dashed line down V on the (0,0) with the shading inside the V.
Answer:
A dashed line down V on the (0,0) with the shading inside the V.
Step-by-step explanation:
- graph of y = -|x| is an upside down V
- less than sign means that there is dashed lines only
- plug in an x-value to determine whether the graph is shaded within the V or outside
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$500 and $550.
Need the answer as a % !!!
Answer:
2.15%
Step-by-step explanation:
If you were to get the z-score for both 500 and 550 and then get the probability of both those z-scores. After getting the probability you would subtract both probability and get your answer.
Z-score:
550-400/2=3
500-400/2=2
Probability:
3 (from the Z-table) is .9987
2 (from the Z-table) is .9772
.9987-.9772= .0215
.0215 as a percentage is 2.15%
Mean: 400
Standard deviation: 50
Check to see if 500 and 550 fall within the standard deviations:
400+2(50) =500
400+3(50) =550
These values lie between the 2nd and 3rd deviations, so
the value is 0.0235
Percentage: 2.35%
Hope it helps!
What is the initial value of the function represented by this table?
Answer: 3
________________________________
initial value = starting value when x is 0
as you can see when x is 0 y is 3
so your initial value is 3
________________________________
Hoped this helped.
An elevator in a tall building goes up 7 floors, then
down a floors, down 4 floors, up 8 floors, and
down 2 floors. Now it is on floor 14. On what
floor did the elevator start?
At the beginning of the school year, Jamie had $500 in her savings account. She wants to have at least $200 left in the account at the end of the school year. Each week, she withdraws $30 for spending money. To determine how many weeks she can spend $30, Jamie wrote and solved this inequality.
The mistake she had done is she should have reversed the inequality as per the division property of inequality.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
The inequality is:
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
Given:
Jamie had $500 in her savings account.
She wants to have at least $200 left in the account at the end of the school year.
The inequality she had done is
500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10
But when she was dividing she should have reversed the inequality as per the division property of inequality.
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K'L'M'N' is a dilation image of KLMN. Which is the correct description of the dilation?
Answer:
d
Step-by-step explanation:
Help plssssss I need this today
Answer:1 is exponential. 2 is linear. 3 is neither. 4 is linear. 5 is linear. 6 is exponential. 7a is exponential. I think 7b could be 10x + y = 10 but I'm not too sure. 7c is (8,4).
Step-by-step explanation:1. the coordinates are moving in an exponential way or something im not sure the correct wording but that is what exponential graphs look like. 2 is a straight line so it is linear. 3 is neither because the graph isn't exponential or linear. 4 is linear because the coordinates are subtracting at the same number. 5 is linear for the same reason at 4. 6 is exponential because the coordinates are multiplied by 2 each time. 7a is exponential because the coordinates are divided by 2 each time. 7b I'm not sure on. 7c is 8/4 because August is the 8th month and the month before (7) is 8 so 8 divided by 2 equals 4. So the 8th month would have to be 4. I hope that helps!
simplify the following polynomial expression. (5^4-9^3+7x-1)+(-8^4x^2-3x+2)-(-4x^3+5x-1)(2x-7)
The simplified expression is 5[tex]x^{4}[/tex] -37 x³ - 6x² +41x -6.
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Given:
(5[tex]x^{4}[/tex] - 9x³ + 7x -1) + ( -8[tex]x^{4}[/tex]+ 4x² - 3x + 2) - ( -4x³ + 5x -1) (2x - 7)
Now,
5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2 - ( -4x³ + 5x -1) (2x - 7)
=5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2-(-8[tex]x^{4}[/tex]+28x³ +10x² - 35x -2x +7
= 5[tex]x^{4}[/tex] - 9x³ + 7x -1 -8[tex]x^{4}[/tex]+ 4x² - 3x + 2 +8[tex]x^{4}[/tex]- 28x³ - 10x² + 35x + 2x - 7
= 5[tex]x^{4}[/tex] -37 x³ - 6x² +41x -6
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Function g is a transformation of function f.
Graph shows 2 exponential functions. First curve f enters quadrant 3 at (minus 6, minus 2) rises through (0, minus 1) and (1, 0) and (2, 2) in quadrant 1. Second curve g enters quadrant 2 at (minus 6, 6) falls through (0, 3) and (1, 0) in quadrant 1.
What is the equation of function g?
g(x) = f(x)
The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given:
genera form of an exponential function is y=aeᵇˣ
Now, equation for f(x) is
f(x) = [tex]e^{(log \;2)x} -2[/tex]
Similarly, graph for g(x) is
g(x) = [tex]-3e^{(log \;2)x} +6[/tex]
Comparing the two function a relation can be establish
g(x) = -3[f(x)]
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Answer:
shifted to the left two units
g(x)=-f(x+2)
Step-by-step explanation:
If point C is between points A and B, then ___ + CB = AB.
A. BC
B. CA
C. ABC
D. AB
Answer:
[tex]\fbox {B. CA}[/tex]
Step-by-step explanation:
Picture the line segment :
⇒ A ---------------- C ------------------ B
Then :
⇒ CA + CB = AB
If 15 members vote to choose 4 group leaders, what is the probability that 4 candidates will be chosen for 4 positions
Answer:
[tex]\frac{4}{60}[/tex] = [tex]\frac{1}{15}[/tex]
Step-by-step explanation:
How do I do this? Subtract the expressions (3x+3)-(4x+6)
Answer:
-x - 3
Step-by-step explanation:
1) Distribute
(3x+3)-(4x+6)
3x + 3 - 4x - 6
2) Subtract the numbers
3x + 3 - 4x - 6
3x - 3 - 4x
3) Combine like terms
3x - 3 - 4x
-x - 3
