Answer:
178.98 square feet
Step-by-step explanation:
Alright so we need to find two areas here and find the difference to find the area of the path.
The two shapes involved is a smaller circle inside a bigger circle.
Let's look at the smaller circle, the gardening area.
You are given is has a radius of 8 ft.
The area of a circle is [tex]\pi \cdot r^2[/tex] where r is the radius.
So the area of the smaller circle is [tex]\pi \cdot 8^2[/tex].
Now time to look at the bigger area (which will have some overlapping area with the smaller one which will subtract out to find the area of path).
The diameter of the smaller circle was (8+8)=16 feet.
What is the diameter of the bigger one. The path is 3 ft wide so we have to add a 3 before the diameter of the smaller circle to another 3 after that diameter to get the diameter of the bigger circle. So the diameter of the bigger circle is (3+16+3)=22 feet. The radius is half the diameter so the radius is 22/2=11.
The area of the bigger circle is [tex]\pi \cdot 11^2[/tex].
The area of the path=
the area of bigger circle - the area of smaller circle=
[tex]\pi \cdot 11^2-\pi \cdot 8^2[/tex]
Type this into your calculator with 3.14 instead of the [tex]\pi[/tex] button.
178.98 square feet
The answer is:
[tex]PathArea=178.98ft^{2}[/tex]
Why?To calculate the are of the path alone, we need to add the width of the path to the radius of the garden in order to know is radius, then, calculate the total area (using garden radius plus path width) and then, subtract it the area of the circular garden.
We know that the radius of the circular garden is equal to 8 feet, and the circular path has a width of 3 feet, so, the radius of the circular path will be:
[tex]CPath_{radius}=8feet+Path_{width}\\\\Path_{radius}=8feet+3feet=11[/tex]
Now, calculating the areas, we have:
Garden Area:
[tex]CircularGardenArea=\pi *radius^{2}\\\\CircularGardenRadius=\pi *8ft^{2}=3.14*64ft^{2}=200.96ft^{2}[/tex]
Total Area:
[tex]TotalArea=\pi *(8feet+3feet)^{2}=\pi *(11ft)^{2}=3.14*121ft^{2}=379.94ft^{2}[/tex]
Now, calculating the area of the path, we have:
[tex]TotalArea=CircularGardenArea+PathArea\\\\PathArea=TotalArea-CircularGardenArea\\\\PathArea=379.94ft^{2}-200.96ft^{2}=178.98ft^{2}[/tex]
Hence, we have that:
[tex]PathArea=178.98ft^{2}[/tex]
Have a nice day!
Which number is equal to 10^4?
40
1,000
10.000
40.000
Answer:
10.000
Step-by-step explanation:
10^4 is equal to 10,000.
10^4 to the second power means that you have too add 4 zeros to the end of the number.
Since 10 already has a 0, you would add 3 more.
Therefore, the answer would be 10,000.
10^4 is the same as saying 10 x 10 x 10 x 10, which is equal to 10 000.
What is the surface area of the figure?
Answer:
0.6625 in²
Step-by-step explanation:
The surface area of this figure will be the area of the base added to area of the triangles
Area of the 4 triangles
Area of a triangle is given by ;
[tex]A=\frac{1}{2} *b*h[/tex]
where b is the base length and h is the height of the triangle
Area of 1 triangle
Given base length as 0.25 inches and height is 1.2 inches.
[tex]A=\frac{1}{2} *0.25*1.2=0.15\\[/tex]
Area of all 4 triangles
- multiply the area of one triangle by 4
- 0.15*4=0.6 in²
Area of the base
The base is a square of length 0.25 inches
Area of a square=length×length
[tex]A=l*l\\A=0.25*0.25=0.0625in^{2}[/tex]
Total surface area
Total surface area= Area of the triangles + Area of the base
[tex]=0.6+0.0625=0.6625in^{2}[/tex]
A writer chargers $5 per word plus a startup fee of $50 per article. Write an equation in standard form to represent the total cost, y of a project that is x words long
Answer:
The answer is y=5x+50
Hope this helps!!!
What is the prime factorization of 621?
Answer:
The prime factors of 621 are 3*3*3*23 ....
Step-by-step explanation:
Prime factorization is the process of finding that which prime numbers can be multiplied together to make the original number.
Find the prime factors of 621.
Start with the smallest prime number which is 2. If the number is divisible by 2 then solve further. If not then move to the next prime number.
621 is nor divisible by 2
We move towards the next prime number which is 3.
621 divided by 3 = 207
207 divided by 3 = 69
69 divided by 3 = 23
Now 23 is only divisible by 23 which is also a prime number.
Thus the prime factors of 621 are 3*3*3*23 ....
So far a total of 48 tickets have been sold for the school play for a total revenue of $220. How many student tickets have been sold? Set up and solve a system of equations to solve the problem.
Adult = $7
Student=$3
Last year you mowed grass and shoveled snow for 10 households. You earned $200 per household
mowing for the entire season and $180 per household shoveling for the entire season. You earn a total of
$1880 last year. Write and solve an algebraic model to determine the number of households you mow and
shovel for
Answer:
what ever it said above
Step-by-step explanation:
Solve for x. Your answer must be simplified. -12x ≤ 44
Answer:
x ≥ - [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Given
- 12x ≤ 44
Divide both sides by - 12, remembering to reverse the inequality sign as a consequence of dividing by a negative quantity, hence
x ≥ [tex]\frac{44}{-12}[/tex] ← note sign reversed
Dividing the numerator/denominator by 4, gives
x ≥ - [tex]\frac{11}{3}[/tex]
Michelle is on a secret mission to reclaim artifacts that were recently stolen from the National Museum. The artifacts are located in a private manor just outside the city. The rectangular base of the manor is 60m by 30m.
Help Michelle plan her mission by redrawing the base of the manor by moving points on the grid below.
HELP!!
The drawing should be 10 units in width and 5 units in height.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
What are problem-solving and examples?Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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A famous instance of variation is Newton’s Law of Gravity. It states that the magnitude of the Force, F, of gravitational attraction between two masses, m1 and m2, varies directly with the product of the masses and inversely with the square of the distance, r, between them. Write a variation equation relating F, m1, m2, and r.
[tex]\bf \qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ F=\cfrac{k(m_1\cdot m_2)}{r^2}\leftarrow \textit{F varies directly with a product and inversely with }r^2[/tex]
What is the name of ostrich's meat?
Answer:
Ostrich meat is a "red meat" similar in color and taste to beef. However, it is lower in fat grams per serving compared to chicken and turkey.
Step-by-step explanation:
Hope this helped??!! :3
What is the equation of the line (in slope-intercept form) that passes through the point (5,−1) and is parallel to the line y=2x−7
Answer:
y = 2x - 11Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\==========================[/tex]
[tex]\text{We have the equation of a line:}\ y=2x-7\to m_1=2.\\\\\text{The slope of a parallel line:}\ m_2=m_1=2.\\\\\text{We have the equation:}\\\\y=2x+b\\\\\text{Put the coordinates of the point (5, -1) o the equation:}\\\\-1=2(5)+b\\-1=10+b\qquad\tex\text{subtract 10 from both sides}\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=2x-11[/tex]
A florist makes a bouquet using 4 roses, 5 carnations, and 3 daffodils.
write the ratio of carnations to daffodils in three different ways.
Answer:
5:3
5 to 3
3/5
There are three ways to write numbers as ratios
As a ratio:
x:y
As a word sentence:
x to y
As a fraction:
x/y
Answer:
The ratio of carnations to daffodils in three different ways are 5/3, 5:3 and 5 to 3.
Step-by-step explanation:
Given information:
Number of roses = 4
Number of carnations = 5
Number of daffodils = 3
We need to write the ratio of carnations to daffodils in three different ways.
The three different ways to write as ratio are
1. Fraction
[tex]\frac{x}{y}[/tex]
2. Ratio using colon
[tex]x:y[/tex]
3. Word form
x to y
The ratio of carnations to daffodils is
[tex]\frac{\text{Number of carnations}}{\text{Number of daffodils}}=\frac{5}{3}[/tex]
It can be written as 5:3 and 5 to 3.
Therefore the ratio of carnations to daffodils in three different ways are 5/3, 5:3 and 5 to 3.
Masha had 200 scoops of ice cream and Liz had 180 scoops. After they each ate an equal amount of scoops, the ratio of Masha’s scoops to Liz’s scoops was 3:2. How many scoops did each of them eat?
Answer:
Each of them eat 140 scoops.
Step-by-step explanation:
Let x be the amount eaten by each of them,
Given,
The initial ice cream Masha has = 200 scoops
Final ice cream Masha has = ( 200 - x ) scoops
while the initial ice cream Liz has = 180 scoops,
Final ice cream Liz has = (180-x) scoops,
According to the question,
[tex]\frac{200-x}{180-x}=\frac{3}{2}[/tex]
[tex]400-2x=540-3x[/tex] ( by cross multiplication )
[tex]-2x=140-3x[/tex] ( Subtracting 400 on both sides )
[tex]x=140[/tex] ( adding 3x on both sides )
Hence, each of them eat 140 scoops.
Answer: 140 scoops.
Hope this helped!
Use the quadratic formula to solve the equation
2x^2- 3x+8 = 0
Answer:
Look at pic.
Step-by-step explanation:
Hope this helps!
Using the quadratic formula, the roots of the equation 2x^2 - 3x + 8 = 0 are found to be complex numbers. The roots are: x = 3/4 ± sqrt(-55) / 4.
Explanation:The subject of this question is the solution to the quadratic equation using the quadratic formula. The quadratic formula is used to find the roots of a quadratic equation, which is an equation of the form ax^2 + bx + c = 0.
The quadratic formula is given by: x = [-b ± sqrt(b^2 - 4ac)] / (2a)
For your equation, 2x^2 - 3x + 8 = 0, the values are a = 2, b = -3 and c = 8.
We substitute these values into the quadratic formula:
x = [3 ± sqrt((-3)^2 - 4*2*8)] / (2*2)
After carrying out the operations, we obtain:
x = [3 ± sqrt(9 - 64)] / 4
The term inside the square root is negative, meaning that the roots of the equation are complex numbers:
x = [3 ± sqrt(-55)] / 4
The answer to the equation is: x = 3/4 ± sqrt(-55) / 4
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The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
Time (hours) Distance (miles)
4 260
6 390
8 520
10 650
Alex and Alicia are twins. Kevin is 5 years older than the twins. Their ages total 53. How old are the twins?
What are the solutions of the equation (x + 2)2 + 12(x + 2) - 14 = 0? Use u substitution and the quadratic formula to solve
x=-8+55
x--653
X=-45_2
x = -2+52
Answer:
[tex]\large\boxed{x=-8\pm5\sqrt2}[/tex]
Step-by-step explanation:
[tex](x-2)^2+12(x+2)-14=0\\\\\text{Substitute}\ (x+2)=t:\\\\t^2+12t-14=0\qquad\text{add 14 to both sides}\\\\t^2+2(t)(6)=14\qquad\text{add}\ 6^2=36\ \text{to both sides}\\\\\underbrace{t^2+2(t)(6)+6^2}=14+36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(t+6)^2=50\Rightarrow t+6=\pm\sqrt{50}\qquad\text{subtract 6 from both sides}\\\\t=-6\pm\sqrt{25\cdot2}\\\\t=-6\pm5\sqrt2[/tex]
[tex]\text{we're going back to substitution}\\\\x+2=-6\pm5\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-8\pm5\sqrt2[/tex]
Creamy Brand ice cream costs $5.50 per gallon, How much would it cost you to buy 2.25 gallons of ice cream for a party if the total tax on your order is $0.72?
Answer:
$13.00
Step-by-step explanation:
so you multiply $5.50 by 2.25 gallons
5.50
x 2.25 =
2750+1100+1100= 12.3750
then you round it off which will make your answer $12.38
then to find out how much it will be with the taxes you add $12.38 and .072 to it to make the total for the ice cream $13.00
Using the horizontal line test, which of the following can be concluded about
the inverse of the graph of the function below?
A horizontal line test on the inverse of a function yields the same results as a vertical line test on the function itself, and the conclusion is the same as in paragraph two.
A vertical line test looks for one or more intersections with a specified set of relations. We can conclude that the relation is a function if there is only one intersection with the relation at ANY point in its domain. If a VERTICAL line intersects the function several times, it is not a function.
Here, we see that the vertical line test on the depicted relation produces just one intersection at any point in the domain of the relation, hence we infer that the graph depicts a function.
A function's inverse is a reflection of the function about the y=x line. The outcome is the same as swapping the x and y axes.
As a result, a horizontal line test on the inverse of a function yields the same results as a vertical line test on the function itself, and the conclusion is the same as in paragraph two.
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What is the value of -3+8 when x=4
is x^2 = 55 irrational or rational
Answer
I think its Rational
Step-by-step explanation:
Answer:
Irrational
Step-by-step explanation:
A rational number can be expressed in the form
[tex]\frac{a}{b}[/tex] where a and b are integers
Given
x² = 55 ( take the square root of both sides )
x = ± [tex]\sqrt{55}[/tex] ← irrational
[tex]\sqrt{55}[/tex] cannot be expressed as a rational number
What is the solution of the equation x2 + 8x + 5 = 0?
Answer:
x = -0.683 (3dp)
x = -7.317 (3dp)
Step-by-step explanation:
Step 1: Apply the quadratic formula
(-b±([tex]\sqrt{b^{2}-4ac}[/tex])) / 2a
a = 1 (x²)
b = 8 (8x)
c = 5 (5)
(-8±([tex]\sqrt{8^{2}-4 x 1 x 5}[/tex])) / 2 x 1
Step 2: Simplify
(-8±([tex]\sqrt{44}[/tex])) / 2
Step 3: Solve
You need to replace the ± with first a + and then a -.
(-8+([tex]\sqrt{44}[/tex])) / 2 = -0.683 (3dp) = x
(-8-([tex]\sqrt{44}[/tex])) / 2 = -7.317 (3dp) = x
Hope this helps!
two numbers are in the ratio of 4:11. their sum is 60. What is the greater of those two numbers?
Answer:
The numbers are 44 (greater) and 16 ( smaler)
Step-by-step explanation:
4x+11x =60
15x = 60
x=4
4*4=16
11*4=44
44+16 = 60
4/11 =0.363636......
16/44= 0.363636......
Average of 6 numbers is 4, if the average of 2 numbers is 2 what is the average of other 4
Answer:
5
Step-by-step explanation:
Let's just pretend the 6 numbers are: a,b,c,d,e,f.
Then (a+b+c+d+e+f)/6 =4 (given by first statement.)
Let's pretend the average of 2 numbers is 2 means they are talking about the a and b.
So (a+b)/2=2.
Now we want to find (c+d+e+f)/4 as requested by their question.
So first step multiply both sides of our first equation by 6 giving us:
a+b+c+d+e+f=24
So the second step multiply both sides of our second equation by 2 giving us:
a+b=4.
Now if a+b+c+d+e+f=24 and a+b=4, then c+d+e+f=20 since 20+4=24.
So the average of the four numbers c,d,e, and f is 20/4=5.
Karen buys 2 packages of printer paper for $5.79 each, a box of pens for $9.25. a box of paperclips for $2.29, and a
calendar for $12.50. If a 6.25% sales tax is added, what is the total cost of Karen's purchase?
(SHOW WORK)
Answer: I think its $37.84625 according to the working shown :)
Step-by-step explanation:
cost of paper= $5.79, hence 2 is 2 x 5.79= 11.58
pens= $9.25
paperclips= $2.29
calendar= $12.50
Total= 11.58+9.25+2.29+12.50= 35.62
6.25% sales tax on total purchase= 6.25/100 x 35.62= $2.22625
Adding the sales tax: 35.62+2.22625= $37.84625
Answer:
$37.84625
Step-by-step explanation:
(5.79*2)+9.25+2.29+12.50=35.62
tax: 6.25% of total cost:
6.25/100 * 35.62=2.22625
total cost + tax
35.62+2.22625=37.84625
What is the x-intercept of the line with the equation y= 1/2 x-3
Answer:
The x intercept is 6
Step-by-step explanation:
To find the x intercept, set y =0 and solve for x
y= 1/2 x-3
0 = 1/2x -3
Add 3 to each side
0+3 = 1/2 x-3+3
3 =1/2x
Multiply each side by 2
2*3 =1/2x*2
6 =x
The x intercept is 6
(Pictures included, pls help)
Carlos draws a transversal, t, on two parallel lines AB and CD, as shown below:
He makes the following table to prove that the alternate interior angles are equal:
Which is The missing justification?
A) Opposite Interior Angles Are congruent when parallel lines are intersecting by a transversal
B) Vertical Angles Formed By Two Intersecting Segments Are Congruent
C) Adjacent Angles Formed By Two Interesting Segments Are Supplementary
D) Opposite Exterior Angles Are Congruent When Parallel Lines Are Intersected By A transversal
Answer:
Option B
Step-by-step explanation:
When two intersecting lines cut each other they form four angles. these two pair of angles are called opposite angles or vertical angles. The vertical angles formed by two intersecting segments are equal.
Thus option B is correct: The vertical Angles Formed By Two Intersecting Segments Are Congruent !
Answer:
B.
Step-by-step explanation:
When you intersect two lines, the angles opposite by the intersection vertex has the same measure. Generally, Those angles are called vertical angles.
In the figure, we have that angle 1 and angle 3 are vertical angles, then both have the same measure. So, the correct option is B) Vertical Angles Formed By Two Intersecting Segments Are Congruent.
What is the verbal expression for 3(n+8)
Make n be a number. You must add 8 and the number together then multiply the answer by 3. This means that the verbal expression is:
3 multiplied by the sum of a number and 8.
Hope this helped!
~Just a girl in love with Shawn Mendes
2sqrt 27 + sqrt12 - 3 sqrt 3 -2 sqrt 12 what is the simplified form of the following expression
Simplified form of expression is,
⇒ - 3√3
We have to given that,
An expression is,
⇒ 2√27 + √12 - 3√3 - 2√12
We can simplify it as,
⇒ 2√27 + √12 - 3√3 - 2√12
⇒ 2 √9×3 + √3×4 - 3√3 - 2√3×4
⇒ 2 × 3 √3 - 2√3 - 3√3 - 2 × 2√3
⇒ 6√3 - 2√3 - 3√3 - 4√3
⇒ - 3√3
Therefore, Simplified form of expression is,
⇒ - 3√3
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Final answer:
The expression simplifies to 4sqrt(3) after breaking down the square roots of 27 and 12 into 3√(3) and 2√(3), respectively, and combining like terms.
Explanation:
To simplify the expression 2√(27) + √(12) - 3√(3) - 2√(12), we should first simplify √(27) and √(12) individually.
Square root of 27 can be written as √(9*3). Since 9 is a perfect square, we get 3√(3). Similarly, √(12) can be simplified to √(4*3). As 4 is a perfect square, this simplifies to 2√(3).
Now, substituting back into the original expression, we get 2(3√(3)) + 2√(3) - 3√(3) - 2(2√(3)), which simplifies to 6√(3) + 2√(3) - 3√(3) - 4√(3).
Combining like terms, we obtain 6√(3) - 2√(3), which simplifies further to 4√(3).
Therefore, the simplified form of the original expression is 4√(3).
the number a is a number less than -3. what is the range of possible values of 1/a squared
Answer:
Numbers less than 1/9.
Step-by-step explanation:
We are given a number [tex]a[/tex] and that it is less than -3.
That is [tex]a<-3[/tex].
What is the range of possibles for [tex]\frac{1}{a^2}[/tex]?
So if [tex]a<-3[/tex] then [tex]a^2>9[/tex].
*I knew to flip inequality here because if I square any number less than -3 it was going have a value bigger than 9.
If [tex]a^2>9[/tex], then [tex]\frac{1}{a^2}<\frac{1}{9}[/tex].
*When taking reciprocal flip the inequality.
Let's do a test:
Let's see if we pick a number less than -3 that we get a result that is less than 1/9 after we find the reciprocal of the square of the number we choose.
Let's pick -4.
-4 is less than -3
Square -4, you get 16 and 16>9.
The reciprocal of 16 is 1/16 and 1/16<1/9.
So 1/16 is a number less than 1/9.
Final answer:
The range of possible values for 1/a squared is all positive numbers greater than 0.
Explanation:
The range of possible values of 1/a squared can be determined by considering the range of values for a. Since a is a number less than -3, it means that a is a negative number less than -3. To find the range of possible values for 1/a squared, we need to consider the range of possible values for a squared. Since a squared is the square of a negative number, it will always be positive. Therefore, the range of possible values for 1/a squared is all positive numbers greater than 0.