Answer:
The perimeter is 48
Step-by-step explanation:
If the width is W
AT first , Length is 10 +w
According to the question,
[tex](w+8) (10+w+4) = 135\\(w+8) (w+14) = 135\\\\w^{2} + 14w + 8w + 112- 135 = 0\\\\ w^{2} + 22w - 23 = 0\\(w+23) (w-1) = 0\\\\w+ 23 = 0 w-1=0\\\\w= -13 or w = 1[/tex]
Expended width will be w +8 = 1+8 = 9
Length is 10+w+4 = 15
So the perimeter is
= i2 x (9+15)
= 2x 24
= 48
The Solution to the problem of the rectangle is given below
For Part A:
equation model: (14 + w) * (w +8) = 132Length = 15For Part B
Perimeter = 46Meaning of Perimeter
The perimeter of any shape can be defined as the total sum of the sides of the shape.
AnalysisFor Part A
equation model= (14 + w) * (w +8) = 135
14w + 112 + 8w + [tex]w^{2}[/tex] = 135
[tex]w^{2}[/tex] + 22w - 23 = 0
solving the quadratic equation
w = -23 or 1
Because we are dealing with a physical quantity we will make use of the value 1
lenght of original rectangle = 10 + 1 = 11
Part B
Perimeter= 2(length) * 2 (breadth) = 2(11 + 4) * 2 (1 + 8)
Perimeter = 48
In conclusion, The Solution to the problem of the rectangle is given above.
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Solve:
x-1
——— < 0
x²-4
Answer: x≠±2, x<±2, x>1, x<1, and x>±2
explanation:
for this equation to be true
Case 1
either (x-1) should be a negative while (x²-4) should be positive
which gives:-
x-1<0
so, x<1
also, x²-4>0
so, x²>4
⇒x>±2
Case 2:-
x-1>0 and x²-4<0
which gives
x>1 and x²-4<0
so, x>1 or x<±2
Case 3:-
either way, the denominator can't be 0
so, x²-4≠0
which gives,
x≠±2
compiling all, we have,
x≠±2, x<±2, x>1, x<1, and x>±2
These solutions can be pointed to as points on a number line and the behavior shows their discontinuity.
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A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14. A hiker in Africa discovers a skull that contains 72 % of its original amount of C 14 .
If the 72% of its original amount of C-14. Then the number of years will be 3285.
The complete question is attached below.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14.
Then the function is given below.
[tex]\rm N= N_0 \ e^{-kt}[/tex]
Where, N₀ is the initial amount of C - 14, t is the number of the years, k is constant that is 0.0001, and N be the amount of the C - 14 at t years.
[tex]\rm N= N_0 \ e^{-0.0001 \times t}[/tex]
We have N = 0.72N₀, the time will be
[tex]\rm 0.72N_0 = N_0 \ e^{-0.0001 \times t}\\\\\rm 0.72 \ \ \ \ = \ e^{-0.0001 \times t}[/tex]
Take log on both side, then we have
ln 0.72 = -0.001 × t × ln e
-0.33 = -0.001 × t
t = 3285 years
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Find the measure of x.
Answer:
25.99
Step-by-step explanation:
SOH CAH TOA
(sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent)
For the angle measurement provided (38 degrees), we know the opposite leg value, and we need to find the hypotenuse
the measurement of sin (opposite / hypotenuse) relates these two measurements
we can plug in our known values into sin:
sin = opposite / hypotenuse
sin (38) = 16 / x
(note: sin 38 = 0.61566147532, which we can round to 0.61566)
0.61566 = 16 / x
· x ·x {multiply both sides by x to get rid of fraction}
0.61566(x) = 16
÷ 0.61566 ÷0.61566 {divide both sides by 0.61566 to isolate 1x}
x = 25.9883702043
{round to nearest hundredth}
x = 25.99
so, the measure of x is 25.99 {rounded to the nearest hundredth}
hope this helps!! have a lovely day :)
Answer:
cosx=adjacent/hypotenuse
triangle angle =180-(90+38)
=52°
cos(52°)=16/x
x=16/cos52
x≈23.373
Please help fast!!
Multiply and reduce to lowest terms. Convert into a mixed number if necessary.
3 x 2/5
Answer:
1 1/5
Step-by-step explanation:
First, make 3 a fraction by putting it over one. Then multiply the numerators (top) together and the denominators (bottom) together.
3/1 x 2/5 = 6/5
Now reduce by dividing 6 by 5 and you get 1 1/5.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3\times\dfrac{2}{5}}\\\\\mathsf{= \dfrac{3}{1}\times\dfrac{2}{5}}\\\\\mathsf{= \dfrac{3\times2}{1\times5}}\\\\\mathsf{= \dfrac{6}{5}}\\\\\mathsf{= 1 \dfrac{1}{5}}\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{\dfrac{6}{5} \ or \ 1 \dfrac{1}{5}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 4 + 2x What does the slope of this function represent? (1 point) a The original height of the plant was 4 mm. b The original height of the plant was 2 mm. c The height of the plant increases by 2 mm for every hour of sunlight it receives. d The height of the plant increases by 4 mm for every hour of sunlight it receives.
The correct answer is option C which is the height of the plant increases by 2 mm for every hour of sunlight it receives.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given equation is as follows:-
y = 4 + 2xHere x is the variable which depends on the amount of sunlight and 4 is the original height of the plant so as the sunlight varies the value of x changes and it increases the height of the plant by 2 mm.
The graph of the equation is also attached with the answer. Therefore the correct answer is option C which is the height of the plant increases by 2 mm for every hour of sunlight it receives.
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What makes the set of intergers different from the set of whole numbers
Answer:
integers include negative numbers, whole numbers are only 0 and positive numbers.
Step-by-step explanation:
whole numbers are very similar to integers as they do not have a decimal place although whole numbers are from 0, 1, 2, 3.... and so on whereas integers include negative numbers as well. So all whole numbers are integers but not all integers are whole numbers.
Find The Distance Between4.5 And -1.4. ( i Need A Answer Right Now Pleaseeeeee!!!!!!
Answer:
5.9
Step-by-step explanation:
The distance between a point A and a point B is A-B. (4.5) - (-1.4) is the same as 4.5 + 1.4 so your answer is 5.9
Answer:
Step-by-steDistance between
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What additional information could be used to prove that the triangles are congruent using aas or asa?.
Answer:
Two angles and a side
Step-by-step explanation:
In order to prove triangles congruent, you'd have to either have an angle, angle, and then a side in that exact order for AAS or you can have two angles and a side in the middle of them for ASA.
A friend of yours, a senior, took the Graduate Record Exam in September and scored in the 99th percentile. In February, your friend took the same exam over again. This time your friend scored in the 90th percentile. As a research methods student, you told your friend that his/her lowered score was most likely due to:
His/her lowered score was most likely due to statistical regression.
How to determine the reason?The missing options in the question are:
A. compensation rivalry B. Demoralization C. Differential selection
D. Testing E. Statistical regression
From the question, we have:
September = 99th percentileFebruary = 90th percentileA change (whether higher or lower) in the score is caused by statistical regression.
This is so because several variables could attribute to the change in the score.
The relationship between these variables is referred to as statistical regression
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QUESTION 10, 11, 12 and 13, 40 POINTS FOR CORRECT AWNSER AND WILL BE BRAINLIEST PLS BE FAST!! I WILL DO ANYTHING U WANT
10. The missing conversion is 20.32 inches
11. Total number of red cars is 34
12. Total number of blue cars is 36
13. Total number of silver cars is 70
What is Ratio?Ratio is the number of times a quantity is contained more or less than another in a whole.
Analysis:
10. If 1 inch = 2.54cm
Then 8 inches = 8 x 2.54cm = 20.32 cm
First car park: Total number of cars = 60
ratio of red:blue:silver = 1:2:3
Total ratio = 1+2+3 = 6
number of red cars = 1/6 x 60 = 10
number of blue cars = 2/6 x 60 = 20 cars
number of silver cars = 3/6 x 60 = 30
second car park: Total number of cars = 80
ratio of blue: red: silver = 2:3:5
total ratio = 2+3+5 = 10
number of red cars = 3/10 x 80 = 24
number of blue cars = 2/10 x 80 = 16
number of silver cars = 5/10 x 80 = 40
11. Total number of red cars = 10+24 = 34
12. Total number of blue cars = 20+16 = 36
13. Total number of silver cars = 30+40 = 70
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This image of a physics problem shows a block resting on a ramp, . ∠P is the angle between the ramp and the horizontal, and is oriented vertically. Which quantity is equal to cos W?
A. sin p
b. cos p
c. 1 - sin p
d. 1 - cos p
Based on the image description, the quantity that is equal to cos W is sin P.
What is the image about?The image is known to be showing an object on a ramp. Based on it, we can therefore take the angle a to the complementary angle of angle w.
Note that the angle w and angle b are said to be the same via alternate interior angles. Therefore, the quantity that is equal to cos W is sin P.
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is n÷12=36,n=108 true or false
Answer:
False
Step-by-step explanation:
n÷12=36
n=36*12
hence n=432
hope it helps you and give me a brainliest
Answer:
(redacted answer - it was wrong - moderator please delete)
false
4. The term containing the highest power of x in the polynomial f(x) is 4x^4. Given that f(x) = 0
has 2 roots -2 and 3, and that 2x² + 3x + 2 is a quadratic factor of f(x),
(a) express f(x) as a polynomial in descending powers of x,
We're given [tex]f(x) = 0[/tex] when [tex]x=-2[/tex] and [tex]x=3[/tex], so both [tex]x+2[/tex] and [tex]x-3[/tex] divide [tex]f(x)[/tex]
We're also told [tex]2x^2+3x+2[/tex] divides [tex]f(x)[/tex]. This quadratic does not have roots at -2 or 3, so we can factorize [tex]f(x)[/tex] as
[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]
where the leading coefficient is 2 because the full expansion should have a leading term of [tex]4x^4[/tex].
Now just expand [tex]f(x)[/tex] :
[tex]f(x) = 2 (x + 2) (x - 3) (2x^2 + 3x + 2)[/tex]
[tex]f(x) = 2 (x^2 - x - 6) (2x^2 + 3x + 2)[/tex]
[tex]f(x) = 2 (2x^4 + x^3 - 13x^2 - 20x - 12)[/tex]
[tex]f(x) = \boxed{4x^4 + 2x^3 - 26x^2 - 40x - 24}[/tex]
Mahek owns a holiday tree farm. There are currently 800 trees on the property. Each year 20% of the trees are harvested and sold, and 200 seedlings are planted. Write a recursive definition for the number of trees on the farm at the beginning of the nth year.
1. a1 = 800, an = 0.20an-1 +200
2. a1 = 200, an = 0.80an-1 + 800
3. a1 = 800, an = 0.80an-1 + 200
4. a1= 0.20, an=0200an-1
The equation of the sequence will be [tex]\rm a_n = 0.8 \times a_{n -1} +200[/tex],
where a₁ = 800. Then the correct option is C.
What is the geometric sequences?Let a₁ be the first term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
Mahek owns a holiday tree farm.
There are currently 800 trees on the property.
Each year, 20% of the trees are harvested and sold, and 200 seedlings are planted.
Then the equation of the sequence will be
[tex]\rm a_n = 0.8 \times a_{n -1} +200[/tex]
Where a₁ = 800.
Then the correct option is C.
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Answer:
3. a1 = 800, an = 0.80an-1 + 200
Step-by-step explanation:
Mila is designing a necklace with 12 platinum spherical beads that each have a radius of 7 millimeters. she has 350 grams of platinum to use. if pure platinum has a mass of 21.5 grams per cubic centimeter, does she have enough to make the 12 spherical beads? explain how you found your answer.
Volume is a three-dimensional scalar quantity. Mila only has 350 grams of platinum, therefore, she does not have enough platinum to make a necklace.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of 12 bead = 12 × (4/3) × π × R³
= 12 × (4/3) × π × (0.7)³
= 17.241 cm³
Given the density of platinum as 21.5 grams per cubic centimeter, therefore,
Mass = density × Volume = 370.682
Since Mila only has 350 grams of platinum, therefore, she does not have enough platinum to make a necklace.
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what is half of 10,000
Answer:
5000
Step-by-step explanation:
1000/2=5000
Let a and b be real numbers where a . Which of the following functions could represent the graph below?
f(x) = x(x – a)3(x – b)3
f(x) = (x – a)2(x – b)4
f(x) = x(x – a)6(x – b)2
f(x) = (x – a)5(x – b)
It can be deduced that the option that represents the graph is B. f(x)=(x-a)²(x-b)⁴
How to solve the graph?From the graph, a and b be real numbers where a = b = 0. In this case, zero is not a root of the polynomial function
When the graph touches the x-axis at two point l, it implies that means that both the roots of the polynomial equation are of even degree.
Thus, the correct option B. i.e. f(x)=(x-a)²(x-b)⁴
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which expressions are equivalent to this exponential expression?
6-10/6-4
A. 6-^6
B. 6^6
C. 1/6^6
D. 1/36
Step-by-step explanation:
Hi There! Let me help you :)
Known
[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]
[tex] \: [/tex]
Asked
Simplify form.
[tex] \: [/tex]
Answer
[tex] = \frac{ {6}^{ - 10} }{ {6}^{ - 4} } [/tex]
[tex] = {6}^{ - 10 - ( - 4)} [/tex]
[tex] = {6}^{ - 6} [/tex]
[tex] = {6}^{ - 6} \: \text{or} \: \frac{1}{ {6}^{6} } [/tex]
There are 2 answers, it's A and C.
Which Expression is Equivalent to (f+g)(4)?
A) F(4) + G(4)
B) F(X) + G(4)
C) F(4 + G(4))
D) 4(F(X) + G(X))
Step-by-step explanation:
[tex] = (f + g)(4)[/tex]
[tex] = f(4) + g(4)[/tex]
The answer is A.
How to write a two column proof for number 12?
1) [tex]\overline{EJ} \parallel \overline{KF}, \overline{JG} \parallel \overline{KH}, \overline{EF} \cong \overline{GH}[/tex] (given)
2) [tex]\overline{FG} \cong \overline{FG}[/tex] (reflexive property)
3) [tex]\overline{EG} \cong \overline{FH}[/tex] (segment addition postulate)
4) [tex]\angle JEF \cong \angle KFG, \angle JGE \cong \angle KHF[/tex] (if two parallel lines are cut by a transversal, the corresponding angles are congruent)
5) [tex]\triangle EJG \cong \triangle F\text{ }KH[/tex] (SAS)
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s? a s = StartFraction 3 Over 10 EndFraction m b s = StartFraction 10 Over 3 EndFraction m c m = StartFraction 3 Over 10 EndFraction s d m = StartFraction 1 Over 30 EndFraction s
The equation which relates the mass and length according to the task content is; l = (3/10)m.
What is the equation of proportionality?From the task content, it follows that the proportional relationship is direct. Hence, the constant of proportionality k can be evaluated as follows;
l = k × m
Hence, k = l/m = 9/30 = 3/10.
Therefore, the proportional relationship is given by the equation; l = (3/10)m
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Which of the following is equivalent to 8-3x > 2(3x - 5) ?
A. 18>9x
B. 9x<13
C. 11>9x
D. -8x>2
Answer:
A
Step-by-step explanation:
Given:
[tex]8-3x > 2(3x-5)[/tex]
Simplify by distributing:
[tex]8-3x > 6x-10[/tex]
Add 10 to left side and add 3x to the right side:
[tex]18 > 9x[/tex]
Solve the following by completing the square y=x^2+10
The resulting equation on using the completing the square is y = (x+5)² - 25
Completing the square methodThe quadratic equation has a leading degree of 2. Given the equation below;
y = x^2+10x
Add the square of the half of coefficient of x to have;
y = x^2+10x + (10/2)²- (10/2)²
y = x^2 + 10x + 5² - 5²
y = x^2 + 10x + 25 - 25
y = (x+5)² - 25
Hence the resulting equation on using the completing the square is y = (x+5)² - 25
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Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.
The average rate of change is 4.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The rate of change in interval [0, 2]
r=[h(2)-h(0)]/2
h(2)=(2)²+2(2)-6
h(2)=4+4-6
h(2)=2
h(0)=(0)²+2(0)-6
h(0)=0+0-6
h(0)=-6
So, r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(8)/2
r=4
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what is the slope of the line that is perpendicular to the line 3y=-5x+21
a -5/3
b -3/5
c- 3/5
d- 5/3
Step-by-step explanation:
the slope is the factor of x in an equation
y = ax + b
we have here
3y = -5x + 21
to get to the general format above we need to divide everything by 3 :
y = -5/3 x + 7
so, we see, the slope is -5/3.
the perpendicular (angle of 90°) slope is the original slope turned upside-down and with flipped sign :
3/5
so, I guess the correct answer option is c.
but it is not clear what you wrote there, as there is a "-" sign somehow in all 4 answers.
y=-6x-8
y=-6x+8
Solve the system of linear equations
Answer: No solution
Step-by-step explanation:
Both of these equations have the same number as to coefficient of x (-6) but have a different constant (-8 and 8). This means that there are no solutions to this system of equations.
PLS HELP
What is the factored form for the quadratic function below?
y = 7x² - 2x - 5
Oy
(7x+5)(x - 1)
Oy
(7x - 5)(x - 1)
Oy (7x + 1)(x + 5)
Oy (7x+5)(x + 1)
Answer: y = (x - 1) (7x + 5)
Step-by-step explanation:
y = 7x² - 2x - 5 Use the slip and slide method.
y = x² - 2x - 35 Factor
y = (x - 7) (x + 5) Slide 7 back in, divide -7 by 7 to get -1. Slip 7 into (x + 5).
y = (x - 1) (7x + 5)
The factorized form of the quadratic equation is y = (7x+5)(x - 1).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
To factor the quadratic function, we need to find two binomials whose product is equal to the given quadratic. Here's one way to factor y = 7x² - 2x - 5:
First, we need to find two numbers whose product is 7(-5) = -35 and whose sum is -2. These numbers are -7 and 5, since (-7)(5) = -35 and (-7) + 5 = -2.
Next, we use these two numbers to split the middle term of the quadratic:
y = 7x² - 7x + 5x - 5
Notice that we have a common factor of 7x in the first two terms and a common factor of 5 in the last two terms. We can factor these out to get:
y = 7x(x - 1) + 5(x - 1)
Now, we have a common factor of (x - 1), which we can factor out to get the factored form:
y = (7x + 5)(x - 1)
Therefore, the correct answer is: y = (7x+5)(x - 1).
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f(x)=|3x +5| +6
g(x) = 7
Find (f + g)(x).
Answer:
(f+g)(x)
= |3x+5| + 13
Step-by-step explanation:
(f+g)(x) means
f(x) + g(x)
so you add the functions together.
|3x+5| + 6 + 7
And simplify.
|3x+5| + 13
A line segment has endpoints Q(-16, -12) and R(21, -8).
What is the midpoint of the line segment?
02¹-201
Answer:
(2.5, - 10 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (- 16, - 12 ) and (x₂, y₂ ) = (21, - 8 ) , then
midpoint = ( [tex]\frac{-16+21}{2}[/tex] , [tex]\frac{-12-8}{2}[/tex] ) = ( [tex]\frac{5}{2}[/tex], [tex]\frac{-20}{2}[/tex] ) = (2.5, - 10 )
Answer: c - (2 1/2 - 10)
Step-by-step explanation:
I need help on this question don't understand this at all
Answer:
F (3)=-1
Step-by-step explanation:
The domain consists of the pre-images and the range has the images. We have the f (3)=-1 since -1 is the image of 3. When we are looking for the function of a number and we are given a diagram of such, we just need to take the value of the number it is pointing to.
