Answer:
The answer is 39 ft so the other person is correct.
Step-by-step explanation:
A fireplace arch is to be constructed in form of a semiellipse. The opening is to have a height of 2 feet at the center and a width of 6 feet along the base. The contractor cuts a string of a certain length and nails each end of the string along the base in order to sketch the outline of the semiellipse.
1. What is the total length of the string?
2. How far from the center should the string be nailed into the base?
Answer:
The total length of the string is 7.85 feet and the center should be 2.236 feet far the string be nailed into the base
Step-by-step explanation:
Circumference of ellipse = [tex]\pi(a+b)[/tex]
Circumference of semi-ellipse = [tex]\frac{\pi(a+b)}{2}[/tex]
we are given that The opening is to have a height of 2 feet at the center and a width of 6 feet along the base.
So, [tex]a = \frac{6}{2}=3 , b = 2[/tex]
Circumference of semi-ellipse =[tex]\frac{3.14(3+2)}{2}=7.85 feet[/tex]
Distance from center =[tex]\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=2.236 feet[/tex]
Hence the total length of the string is 7.85 feet and the center should be 2.236 feet far the string be nailed into the base
9. Given f(x) and g(x), find f(g(3))
f(x) = x2 +9
g(x) = x - 7
O A) -13
O B) 25
O C) 11
OD) 2
=============================================
Work Shown:
g(x) = x-7
g(3) = 3-7 .... replace every x with 3
g(3) = -4
f(g(3)) = f(-4) .... replace g(3) with -4
f(x) = x^2+9
f(-4) = (-4)^2+9
f(-4) = 16+9
f(-4) = 25
f(g(3)) = 25
-------------------------
Another approach:
f(x) = x^2 + 9
f( g(x) ) = ( g(x) )^2 + 9 ... replace every x with g(x)
f( g(x) ) = ( x-7 )^2 + 9 ... plug in g(x) = x-7
f( g(3) ) = ( 3-7 )^2 + 9 .... plug in x = 3
f( g(3) ) = ( -4 )^2 + 9
f( g(3) ) = 16 + 9
f( g(3) ) = 25
Show why 4y + 6 < 38 and -3x - 6 > 18 are considered equivalent
inequalities
Answer:
undefenide+
Step-by-step explanation:
0e46.38 times 6.1 = undefenide+
I hope thishelped your question and have a big A +
byeee✍✍✍
What is 62% of 500 ? ?
Answer:
310
Step-by-step explanation:
Answer: 310
Step-by-step explanation: 2% equals 10, so just keep counting up until you get 62%.
Hopefully this helped! :D
Laura spent 78.5% of her paycheck on her mortgage payment. If her paycheck was $1562 how much was her mortgage?
Answer:
$337.12
Step-by-step explanation:
Multiply $1562 by 78.5% (or 0.785) =1230.88
Then subtract the percent of her paycheck spent (1230.88) from the total of her paycheck(1562) to find out how much is missing(the mortgage payment)
1562-1230.88=337.12
Donovan rode 135 miles on his bike at a unit rate of 27 miles per hour. How many hours did he spend riding?
Answer:
5 HOURS
Step-by-step explanation:
Answer:
5 hours
Step-by-step explanation:
if x^2-x-6 and x^2+3x-18 hacpve a common factor (x-a) then find the value of a.
Answer:
a = 3
Step-by-step explanation:
Factor both expressions
x² - x - 6
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 1)
The factors are - 3 and + 2 , since
- 3 × 2 = - 6 and - 3 + 2 = - 1 , thus
x² - x - 6 = (x - 3)(x + 2)
-----------------------------------
x² + 3x - 18
consider factors of constant term (- 18) which sum to give the coefficient of the x- term (+ 3)
The factors are + 6 and - 3 , since
6 × - 3 = - 18 and 6 - 3 = + 3 , thus
x² + 3x - 18 = (x + 6)(x - 3)
Both expressions have a common factor of (x - 3)
Compare with (x - a ), then a = 3
Please help!!! Use the digital to answer the question above
Answer: 16
Step-by-step explanation: The angles are equal so x+24 = 3x-8
What is the first step needed to solve 3 over 4 multiplied by x minus 3 equals negative 18 ? (1 point)
Add 3 to both sides
Subtract 18 from both sides
Multiply both sides by 3
Divide both sides by 4
Answer:
Divide both sides by 4
Step-by-step explanation:
Answer:
i just took the test and it was divide by 4 sides
Step-by-step explanation:
what is the constant in the expression 13x3+x2-4x+8
Answer:8
Step-by-step explanation:
it is the only one without a variable.
Answer:
[tex]\boxed {\tt 8}[/tex]
Step-by-step explanation:
A constant is a term without a variable.
Let's analyze each term of the expression: 13x³+x²-4x+8
13x³: this has a variable of x³
x²: this has a variable of x²
-4x: this has a variable of x
8: this has no variable
Since 8 is the term without a variable, 8 is the constant.
PLZZZZZ HELP NEEDED ASAP WILL GIVE BRAINLIEST (IF RIGHT)
Lines AB and CD are straight lines. Find x and y. Give reasons to justify your solutions.
x= 90° - 63° = 27° (NO perpendicular to AOB)
angle DOB = (90°+90°) -128° (angles on a straight line)
= 180° - 128°
= 52°
y= 180° - x - 63° - angle DOB (angles on a straight line)
=180° - 27° - 63° - 52°
= 38°
I'm not sure of the answer tho^^ good luck!
Which equation can be used to graph the line that passes through (6, 15) and is perpendicular to the graph of y-7=1/2(x+2)
Answer:
y = -2x + 27
Step-by-step explanation:
Firstly, we shall need to reform the given line equation;
y-7 = 1/2 ( x + 2)
y - 7 = x/2 + 1
y = x/2 + 1 + 8
y = x/2 + 8
Comparing this with y = mx + c
where m is the slope, then the slope of the line is 1/2
Since the line we are looking for has a slope perpendicular to this line, it means that the product of their slopes is -1
m1 * m2 = -1
1/2 * m2 = -1
m2 = -2
So we want an equation with slope -2 passing through (6,15)
we use the point slope method here;
y-y1 = m(x-x1)
y-15 = -2(x-6)
y-15 = -2x + 12
y= -2x + 12 + 15
y = -2x + 27
identify the domain and the range of the function
So the first graph is Radical/Irrational Graph and the second is Parabola/Quadratic Graph.
You can find the domain by looking at the x-axis and for the range, look at the y-axis. That means all of x-axis is the domain and all of y-axis is the range.
From the first graph, the domain is from -2 to +infinite. But because there's a colored dot, it's either ≥ or ≤.
But because -2 is less than + infinite, we use ≤ instead. Thus, x ≥ -2
Remember that x-values can't be equal to infinite. So we use < instead since there's no x-values that are equal to ∞.
Or we can write in interval notation as [-2,+∞) for symbol "[ or ]" is equal to ≤ or ≥ and ") or (" is equal to > or <
Again, the domain for the first graph is x ≥ -2 or x ∈ [-2, +∞)
And the range, look at the y-axis. Because we can substitute x from -2 to less than ∞, that means the range is from -1 because when x = -2 then x = -1 to + infinite.
Therefore, the range is y ≥ -1 or y ∈ [-1, +∞)
Now for the second graph. Look at the x-axis to find the domain. We notice that the colored dot is at x = -3 and the one with white dot is at x =2. The one without the color or white dot is > or < while the colored one is ≥ or ≤.
So the domain is -3 ≤ x < 2 or x ∈ [-3, 2)
For range, look at the y-axis. Notice that the colored dot is at y = -5 and the maximum point is at y =4. The y =4 is still in the domain so the range still applies to the maximum point.
Therefore the range is -5 ≤ y ≤ 4 or y ∈ [-5, 4]
The following expression represents the population of colony of penguins in Antarctica: P,= 17.2.3 P, is the penguin population, and r is time in days. a. What is the population after 6 days? b. When will P, be 650 penguins?
Graph the inequality.
y2-3x+4
a store has a outfit that is $35.00 and 50% of what is the price now.
Answer:
$70Step-by-step explanation:
The price is x
50% of the price is $35
x*0.5 = 35x = 35/0.5x = 70Answer is $70
Answer:
$17.50Step-by-step explanation:
50% off the price of $35
= $35 ( 0.50)
= $17.50 (price now)
need help with 4 ASAP
please help me I would also like an explanation
Answer:
k = 45*
2k = 90*
Step-by-step explanation:
K will be the same as the 45* degrees, as it is across from it.
2k is twice k, which is 90*.
45* + 45* + 90* = 180*
Good luck!
There are 3 times as many females as males on the maths course at university. What fraction of the course are male?
Give your answer in its simplest form.
Answer:
1/3
Step-by-step explanation:
Because I’m right
Write an inequality for the situation: the sum of two numbers is less than 5.
3. Sophie solved the inequality
as shown. Explain Sophie's error
and give the correct solution to
the inequality.
-5(x - 1) > -7x + 19
-5X - 5 >-7x +19
2x - 5 > 19
2x > 24
X>12
Answer:
After she distribute the [tex]x[/tex] and [tex]-1[/tex] by [tex]-5[/tex], the after you get [tex]-5x - 5 > -7x + 19[/tex], she put a negative [tex]5[/tex] instead of a positive [tex]5[/tex], and would be written as[tex]-5x + 5 > -7x + 19[/tex].
Step-by-step explanation:
Solve the inequality for the correct solution:
[tex]-5(x - 1) > -7x + 19[/tex]
-Use Distributive Property:
[tex]-5(x - 1) > -7x + 19[/tex]
[tex]-5x + 5 > -7x + 19[/tex]
-Take [tex]7x[/tex] and add it to [tex]-5x[/tex]:
[tex]-5x + 5 + 7x > -7x + 7x + 19[/tex]
[tex]2x + 5 > 19[/tex]
-Subtract [tex]5[/tex] to both sides:
[tex]2x + 5 - 5 > 19 - 5[/tex]
[tex]2x > 14[/tex]
-Divide both sides by [tex]2[/tex]:
[tex]\frac{2x}{2} > \frac{14}{2}[/tex]
[tex]\boxed {x > 7}[/tex]
compare 249 and 271 write the greatest number in word form.
Answer:
271>249
Two hundred seventy-one is greater than two hundred forty-nine
I don't know if you should only write the bigger number
Answer:
3.7/5. 6.
Step-by-step explanation:
if f(x)= -6x + 2, what is f(-1)
Answer:
f(-1) = 8
Step-by-step explanation:
Step 1: Define
f(x) = -6x + 2
f(-1) is x = -1
Step 2: Substitute and Evaluate
f(-1) = -6(-1) + 2
f(-1) = 6 + 2
f(-1) = 8
Answer:
8
Step-by-step explanation:
Substitute -1 for x
-6(-1) + 2
Simplify
6+2
Simplify
8
One fifth of r is fifteen what is r
Answer:
75.
Step-by-step explanation:
r = 15
r = 1/5 of x
15*5=75
x = 75
Help please :( find x
Answer:
x = 33
Step-by-step explanation:
The sum of a quadrilateral adds up to 360°.
Step 1: Set up equation
98 + 98 + 98 + 2x = 360
Step 2: Solve for x
Combine like terms: 294 + 2x = 360Subtract 293 on both sides: 2x = 66Divide both sides by 2: x = 33The length y of a rectangle is four less than three times the width x. The perimeter of the rectangle is 16 cm. Write a system of equations to represent this situation and find the dimensions of the rectangle. PLEASE PLEASE HELP MEEE IF I DONT ANSWER IM GOING TO GET KICKED OUT OF THE COURSE PLEASEEEEE HELPP
Answer:
L=5
w=3
Step-by-step explanation:
Length = 3x+4
2L+2W=16
plug in 3x+4 into L
2(3x+4)+2x=16
6x-8+2x=16
6x+2x=16+8
then just do basic algebra
8x=24
divide 24/8
x=3 is the width
5 is the length
L=5
w=3
An aquarium is on on sale for $59.50. If this represents a 15% discount from the original price, what is the original price to the nearest cent.
Answer:$68.43
Step-by-step explanation:
An industrial printing machine printed 1764 pages in 6 minutes. How much would it have printed in 4 minutes?
Answer:
1176
Step-by-step explanation:
i hope this helps out
4x - 7 <-35
Please help
Answer:
x < -7
Step-by-step explanation:
treat is like a normal equation when solving, solve using inverse operations
4x - 7 < -35
+7 +7
4x < -28
/4 /4
x < -7
what’s the slope please help me
Answer:
-1
Step-by-step explanation:
The slope goes down 1 as it goes over (to the right) 1
Answer:
-1 would be the slope.
Step-by-step explanation:
Using rise over run, the slope would be -1.