The 34 feet perimeter and width, x, of the window which is in the shape of a rectangle surmounted by a semicircle is, A = 17•x - x²•(1/2 - π/8)
How can the area of the window be expressed as a function of x?The shape of the window = A rectangle surmounted by a semicircle
Perimeter of the window, P = 34 feet
Width of the window = x
Required; The area, A, of the window as a function of x
Solution:
Diameter of the semicircle = x
Length of the semicircular arc = π•x/2
Let y represent the height of the window, we have;
P = 2•y + x + π•x/2 = 34
Therefore;
y = (34 - (x + π•x/2))/2 = 17 - x•(1 + π/2)/2
Area of the window, A = x × y + π•x²/8
Which gives;
A = x × (17 - x•(1 + π/2)/2) + π•x²/8 = 17•x - x²/2 - x²•π/8
A = 17•x - x²/2 - x²•π/8 = 17•x - x²•(1/2 - π/8)
Therefore;
Window area, A = 17•x - x²•(1/2 - π/8)
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The table below models a particular physical situation.
x −9, −3, 4 ,10
y 9, 1, −7, 10
Find the piecewise linear equation that models the data above. Round to three decimal places if needed.
y={
___ x + ___. −9 ≤ x ≤ −3
___ x + ___. −3 < x ≤ 4
___ x + ___. 4 < x ≤ 10
Answer:
Step-by-step explanation:4
Step-by-step explanation:
We do the ones that are in parenthesis first. Find out the exponent. 2 to the power of two is 4. 3-4=-1. Then we would add 5. 5+-1 would result of 4.
The ratio of saving to spending is 9:4 how does she spend and how mush does she save
She will spend £250 and save £400.
Ratio is an expression that indicates how many times one quantity is more than the other.
Here, we are given that Miss penny inherits £650.
Her saving to spending ratio is 9 : 4
Thus, the proportion of money she saves is 9/ (4+9) = 9/13
therefore, the amount of money saved will be-
9/13 of 650
= 9/13 * 650
= 9 * 50
= 450
Thus, Miss Penny saves £400.
The remaining amount left with her = 650 - 400 = 250.
Thus, she spends the remaining £250.
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Your question was incomplete. Check for full content below-
Miss penny inherits £650. She decides to save some of the money and spend the rest. The ratio of saving to spending money is 9:4. How much does she save and how much does she spend?
Order the cube root of 37, 16 over 5, negative four and two thirds, and negative pi from greatest to least.
the cube root of 37, 16 over 5, negative pi, and negative four and two thirds
16 over 5, the cube root of 37, negative four and two thirds, and negative pi
16 over 5, the cube root of 37, negative pi, and negative four and two thirds
the cube root of 37, 16 over 5, negative four and two thirds, and negative pi
The order of the numbers from greatest to smallest is the cube root of 37, 16 over 5, negative pi, and negative four and two thirds
What is the order of the numbers?The numbers we are to order from the greatest to the least are ∛37, 16/5, -4 2/3, -22/7. To ease the problem, all the numbers should be converted to decimal form.
A decimal is a number that consists of integers and non-integers. The integers are separated from the non-integers by a decimal point. An example of a decimal number is 1.23.
When converted to decimals, the number become:
∛37 = 3.33
16/5 = 3.2
-4 2/3 = -14/3 = -4.67
-22/7 = -3.14
The further away a positive number is from zero, the greater the number. The closer a negative number is to zero, the greater the number.
3.33, 3.2, -3.14, -4.67
∛37, 16/5, - 22/7, -4 2/3
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Answer:
The person above was correct! gl on ur exam :))
Given the function ()=−4‾‾‾‾‾‾√,
g
(
m
)
=
m
−
4
,
evaluate
The required solution is 1(one) as per the given functions.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the sphere of the function and the set Y is called the codomain of the function. Functions were firstly the idealization of how a varying volume depends on another volume, an expression, rule, or law that defines a relationship between one variable( the independent variable) and another variable( the dependent variable). Functions were firstly the idealization of how a varying volume depends on another volume. For illustration, the position of the earth is a function of time.Every function has a(one) domain and codomain or range. A function is generally(ax) denoted by f(x) where x(ax) is the input
Given :
The function(one)
g(m)= m-4(four).
By put m is equal to 5(five) we get,
g(5)=5-4(four)
=1(one)
Hence, the required solution is 1(one) as per the given functions.
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Which fraction is less than 1 chose all of the correct answer, and explain why you chose and write it down and explain your answer. 7/6 5/6 3/4 2/3 6/4 5/3 explain why you got that answer.
Answer:
[tex](3/4)[/tex] and [tex](2/3)[/tex].
Step-by-step explanation:
For a fraction of the form [tex](p / q)[/tex], the number in front of the division ([tex]p[/tex]) is the numerator. The number after the division ([tex]q[/tex]) is the denominator.
[tex]\begin{aligned} \frac{p}{q} \quad \genfrac{}{}{0}{}{(\text{numerator})}{(\text{denominator})}\end{aligned}[/tex].
A positive fraction [tex](p/q)[/tex] ([tex]p,\, q > 0[/tex]) is less than [tex]1[/tex] as long as the numerator [tex]p[/tex] is smaller than the denominator [tex]q[/tex] (that is, [tex]p < q[/tex].) The reason is that as long as [tex]p,\, q > 0[/tex]:
[tex]\begin{aligned} & \frac{p}{q} < 1 \\ \iff & (q)\, \left(\frac{p}{q}\right) < (q)\, (1) && (\text{given that $q > 0$}) \\ \iff & p < q\end{aligned}[/tex].
For example, in the fraction [tex](2/3)[/tex], [tex]2[/tex] is the numerator while [tex]3[/tex] is the denominator. Both the numerator and the denominator are positive, while the numerator [tex]2\![/tex] is smaller than the denominator [tex]3\![/tex]. Therefore, [tex](2/3)[/tex] would be less than [tex]1[/tex].
Melissa is simplifying an expression using the order of operations. She adds 3 and 4, squares the result, and subtracts 9. Which expression is Melissa simplifying? (3+4-9)², 3+4²-9, 3²+4²-9, (3+4)² - 9
we get that Melissa is trying to solve the expression ( 3 + 4) ² - 9.
We are given that:
Melissa is simplifying an expression using the order of operations which can be addition, subtraction, multiplication or division.
She adds 3 and 4, squares the result, and subtracts 9.
We will first add 3 and 4:
3 + 4
Now we will square them:
( 3 + 4) ²
Now, we will subtract 9 from it:
( 3 + 4) ² - 9
So, the expression becomes:
( 3 + 4) ² - 9
Therefore, we get that Melissa is trying to solve the expression ( 3 + 4) ² - 9.
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When you draft a budget, you should include an _________________. This is extra money set aside to be used for unpredictable expenses, such as medical bills and vehicle repairs.
Group of answer choices
annual expenses
expense summary
fixed expenses
Emergency fund
Answer:When you draft a budget, you should include an _________________. This is extra money set aside to be used for unpredictable expenses, such as medical bills and vehicle repairs
Step-by-step explanation:
What is 22 divided 2.630 and what’s the remainder
Answer:
22 divided by 2.630= 8 remainder 0.96
Answer: 22/2.630 is 8, remainder is 0.365 or 73/200
Which is the best approximation for the solution of the system of equations?
y= -2/5x + 1
Y = 3x -2
A: (0.45, 0.88)
B:(0.88, 0.65)
C:(0.88, 1.11)
D:(1.3, 0.88)
Graph pictured below
What does 1/4+2/3 equal
Answer:
[tex]\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]Rule: \frac{x}{y} \pm \frac{a}{b} = \frac{x \pm y}{z}\\\frac{1}{4}+\frac{2}{3} = \frac{3}{12}+\frac{8}{12} (LCM)\\=\frac{3+8}{12}\\=\frac{11}{12}\\[/tex]
Can someone ppl me lease help me with this question and not text me ab random stuff… :/
Answer:
{2,3,5,6,8}
Step-by-step explanation:
U={1,2,3,4,5,6,7,8}
A{3,4,5,6}
B{1,4,8}
C{2,3,4,5,6}
We are to find
{A' n B} U {A' n C'}
={3,5,6,8}. U. {2}
= {2,3,5,6,8}
(a) Use the iteration formula +1=10-2x, to find the values of X₁, X2 and xs
Start with Xo = 2
The value for the given question is x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.
Given iteration formula as xₙ ₊ ₁ = ∛ 10 - 2xₙ
Given x₀ = 2
We have to find the values of x₁, x₂, and x₃ as
For finding the value of x₁ we need to substitute n = 0 as
xₙ ₊ ₁ = ∛ 10 - 2xₙ
x₀ ₊ ₁ = ∛ 10 - 2x₀
x₁ = ∛ 10 - 2(2) (∵ x₀ = 2)
x₁ = ∛ 10 - 4
x₁ = ∛ 6
x₁ = 1.8
For finding the value of x₂ we need to substitute n = 1 as
xₙ ₊ ₁ = ∛ 10 - 2xₙ
x₁ ₊ ₁ = ∛ 10 - 2x₁
x₂ = ∛ 10 - 2(1.8) (∵ x₁ = 1.8)
x₂ = ∛ 10 - 3.6
x₂ = ∛ 6.4
x₂ = 1.85
For finding the value of x₃ we need to substitute n = 2 as
x₂ ₊ ₁ = ∛ 10 - 2xₙ
x₂ ₊ ₁ = ∛ 10 - 2x₂
x₃ = ∛ 10 - 2(1.85) (∵ x₀ = 1.85)
x₃ = ∛ 10 - 3.7
x₃ = ∛ 6.3
x₃ = 1.846
Therefore, the value of x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.
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2. ¿Qué probabilidad hay de extraer una A seguida de una M de las letras de la
palabra MATEMÁTICAS (sin devolución)?
Usando su concepto, se encuentra que hay una probabilidad de 3/55 de extraer una A seguida de una M de las letras de la palabra MATEMÁTICAS.
¿Qué es una probabilidad?Una probabilidad viene dada por el número de resultados deseados dividido por el número de resultados totales.
En este problema, hay que:
De las 11 letras, 3 son A.De las 10 letras restantes, 2 son M.Asi:
p = 3/11 x 2/10 = 3/55
Hay una probabilidad de 3/55 de extraer una A seguida de una M de las letras de la palabra MATEMÁTICAS.
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Solve: x0.09=0.81. Round to the hundredths place. Do not include "x=" in your answer.
The value of x in the equation x0.09 = 0.81 is 9
How to determine the value of x?The equation is given as
x0.09 = 0.81
Rewrite the above expression properly
So, we have:
x * 0.09 = 0.81
Divide both sides by 0.09
So, we have:
x = 0.81/0.09
Evaluate
x = 9
Hence, the value of x in the equation x0.09 = 0.81 is 9
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HELP PLS, I NEED AN ANSWER ASAP, 25 POINTS AVALIABLE
The gradient of the line y = x/3 - 4 is; 1/3
What is the gradient of the given line?
Slope is defined as the gradient of a graph at any point
We are given the equation of the line as;
y = x/3 - 4
Now, the formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, from the given equation, we can tell that the gradient which is the slope is 1/3.
Thus, we conclude that the gradient of the line y = x/3 - 4 is; 1/3
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The larger room is twice as wide as the smaller room which is 29 3/4’. How wide is the
larger room?
Answer: 59.5
Step-by-step explanation: 29 3/4 times 2
I think
0.007349 to three significant figures
Answer:
Step-by-step explanation:
From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.
0.007349 to 3 significant figure=0.00735
f(x)=x+2
g(x) = 3x² - 5
Find (f ·g)(x).
Step-by-step explanation:
f(x) = x + 2
g(x) = 3x² - 5
= (f.g)(x)
= (x + 2).(3x² - 5)
= 3x³ - 5x + 6x² - 10
= 3x³ + 6x² - 5x - 10
O-13
13
O-5
O 5
Simplify 9-(-4)=
Answer:
B. 13
Step-by-step explanation:
[tex]Rule:a-\left(-b\right)=a+b\\=9-\left(-4\right)=9+4\\=9+4\\=13[/tex]
Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
The time it would take Shirley to mow the lawn alone is 3 hours
How to determine the value
From the information given;
Let Shirley's working hours be x
Let Pam's working hours be y
We have that;
Shirley and Pam work 6 hours together, this is expressed as;
x + y = 6
Given that Pam work 3 hours alone, we have;
y = 3
Substitute the value of y as 3 in the equation
x + 3 = 6
x = 6 - 3
x = 3
Thus, the time it would take Shirley to mow the lawn alone is 3 hours
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write 336 mi in 11.2 h as a rate in simplest form
Answer:
30 mL/h
Step-by-step explanation:
You want the rate 336 ml in 11.2 h as a rate in simplest form.
Unit rateThe rate can be expressed in simplest form in a number of ways. We usually want rates involving time to be expressed with time units in the denominator:
(336 mL) / (11.2 h) = 30 mL/h
__
Additional comment
Medicine is often prescribed on a "per day" basis. In 24 hours, this rate would be ...
(30 mL/h)×(24 h/day) = 720 mL/day
The machine setup to dispense this medicine might use time units of minutes:
(30 mL/h) / (60 min/h) = (1/2) mL/min
Select the expression that has a quotient greater than 1. Explain your reasoning PLEASE ANSWER THIS
1. 4 2/3 ÷ 5 1/4
2. 3 1/8 ÷ 2 2/5
3. 1 6/7 ÷ 2 1/3
4. 5 3/4 ÷ 7 3/8
Two children weigh 160 pounds together the oldest weighs 120 pounds more how much do they each weigh 
what is the place value?
If you only have a 1/3 measuring cup and a recipe calls for 12 2/3 cups of flour, how many 1/3 cups would you need to use? 1/3 * t th cups
====================================================
Explanation:
Imagine drawing a circle and splitting it into 3 equal slices. Repeat this process to get 12 identical such circles. We have 12*3 = 36 slices so far.
Then add a 13th circle that has 2 of the 3 slices shaded, to represent 2/3. So we add 2 extra slices to the 36 original to get 36+2 = 38 total slices.
Each slice represents 1/3 of a cup. So each full circle represents 1 full cup.
-------------
Another approach:
Let's convert the mixed number 12 & 2/3 into an improper fraction
We use the formula
a & b/c = (a*c+b)/c
So,
12 & 2/3 = (12*3+2)/3 = (36+2)/3 = 38/3
Then rewrite the 38/3 as 38*(1/3) to show we have 38 copies of the 1/3 cup.
Answer: 38 cups
Step-by-step explanation:
We will divide 12 2/3 cups by our measurement, 1/3 cup, to find how many 1/3 cups will be needed.
(12 + 2/3) / (1/3) = 38 cups
Suppose that the x-intercepts of the graph of y = f(x) are -5 and 3. . a) What are the x-intercepts of the graph of y = 7f(x)?
Answer:
[tex](-5)[/tex] and [tex]3[/tex].
Step-by-step explanation:
The [tex]x[/tex]-intercepts of a graph refer to points where the graph intersects the [tex]x\![/tex]-axis. These are [tex]x\!\![/tex] values for which [tex]f(x) = 0[/tex].
For example, since [tex]x = (-5)[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)[/tex], it must be true that [tex]f(-5) = 0[/tex]. Likewise, since [tex]3[/tex] is one of the [tex]x[/tex]-intercepts of [tex]y = f(x)\![/tex], [tex]f(3) = 0[/tex].
Since [tex]f(-5) = 0[/tex], the expression [tex]7\, f(-5)[/tex] would also evaluate to [tex]0[/tex] (that is, [tex]7\, f(-5) = (7)\, (0) = 0[/tex].) Thus, [tex]x = (-5)[/tex] would be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].
Likewise, since [tex]f(3) = 0[/tex], [tex]7\, f(3) = (7)\, (0) = 0[/tex], such that [tex]x = 3[/tex] would also be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex].
No other points could be an [tex]x[/tex]-intercept of the new graph [tex]y = 7\, f(x)[/tex] without being an [tex]x\![/tex]-intercept of [tex]y = f(x)[/tex]. For example, assume that [tex]x = x_{0}[/tex] is an [tex]x[/tex]-intercept of [tex]y = 7\, f(x)[/tex] but not [tex]y = f(x)[/tex]. [tex]7\, f(x_{0}) = 0[/tex], such that [tex]f(x_{0}) = (1/7)\, (7\, f(x_{0})) = (1/7)\, (0) = 0[/tex]- contradiction.
Therefore, the [tex]x[/tex]-intercepts of the new graph would be [tex]x = (-5)[/tex] and [tex]x = 3[/tex].
Evaluate h(r) given that h(t) = 6 - 18t. h(r) =
This problem is related to the formation of a function. We need to know how an function is formed. Here it is given that there is a function which is affected by the value of t. Which means the value of t in the function decides the value of that function.
Similarly we have to write the function as the variable r so that the value of function is related to the value of r.
h(r)=6-18r ; where 6 is the constant and 18r is the variable in the function.
Hence, the required function is h(r)=6-18r.
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The table shows the side lengths and perimeters of four squares.
Side Length (x)
Perimeter (y)
4.5
18
8.5
34
10.25
41
13.75
55
Which equation represents the relationship between the side length, x, and the perimeter, y?
y = one-fourth x
y = 4x
y = x + 13.5
y = x – 13.5
Answer:
12 ×13.5 y 13.5
Step-by-step explanation:
es igual a 400
Answer:
y=4x
Step-by-step explanation:
Solve x/4>_-1 and -4x-4<_-3 and write the solution in interval notation. If there is no solution, type the no solution symbol.
The solution interval for x is x ∈ (-1/4 , ∞)
An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.
Here, we are given two inequalities
x/4 > -1 and -4x - 4 < -3
Let us take the first equation
x/4 > -1
⇒ x > 4(-1)
x > -4
Now, the second equation
-4x - 4 < -3
-4x < -3 + 4
-4x < 1
Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,
x > 1/-4
x > -1/4
Thus, we get x > -4 and x > -1/4
This means that all values of x greater than -1/4 will satisfy.
Thus, x ∈ (-1/4 , ∞)
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How long would it take for a ball dropped from the top of a 121-foot building to hit the ground? Round your answer to two decimal places.
I don't need to know the actual answer, I'm just not sure what to plug in where into this formula: h=-½gt^2 +v0t+h0
The time that it will take the ball to hit the ground in 4 seconds.
How to solve equation of motion?To solve this problem you need the function;
h(t) = -16t² + v₀t + h₀
where;
t = time
v₀ is the initial velocity, which in our case is 0
h₀ is initial height, which in our case is 121 ft
h(t) = 0 since we want to know when the ball will hit the ground.
Thus;
0 = -16t² + 121
And we can solve for t;
If we rearrange the terms we see that this is a difference of 2 squares
0 = 121 - 16t²
0 = (11 - 4t)(11 + 4t)
Setting each factor = 0 gives;
11 - 4t = 0 11 + 4t = 0
t = 11/4 or t = -11/44
The second solution is discarded as time cannot be negative.
Thus, the ball will hit the ground in 4 seconds.
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