Answer:
74.8 square yards
Step-by-step explanation:
The centerline of the path is a rectangle 5.3+2 = 7.3 yards wide and 9.4+2 = 11.4 yards long. The perimeter of that rectangle is 2(7.3+11.4) = 37.4 yards long. The area of the path is this length times the width of the path:
path area = (37.4 yd)(2 yd) = 74.8 yd²
The area of the path is 74.8 square yards.
First, we calculate the area of the garden:
[tex]\[ A_{\text{garden}} = \text{length} \times \text{width} = 9.4 \text{ yards} \times 5.3 \text{ yards} \][/tex]
[tex]\[ A_{\text{garden}} = 49.82 \text{ square yards} \][/tex]
Next, we need to find the area of the entire region including the path. The path adds an additional width of 2 yards on all sides of the garden.
The total length and width of the region including the path are:
[tex]\[ \text{Total length} = 9.4 \text{ yards} + 2 \times 2 \text{ yards} = 13.4 \text{ yards} \][/tex]
[tex]\[ \text{Total width} = 5.3 \text{ yards} + 2 \times 2 \text{ yards} = 9.3 \text{ yards} \][/tex]
Now we calculate the area of the entire region including the path:
[tex]\[ A_{\text{total}} = \text{Total length} \times \text{Total width} = 13.4 \text{ yards} \times 9.3 \text{ yards} \][/tex]
[tex]\[ A_{\text{total}} = 124.62 \text{ square yards} \][/tex]
Finally, we subtract the area of the garden from the total area to find the area of the path:
[tex]\[ A_{\text{path}} = A_{\text{total}} - A_{\text{garden}} \][/tex]
[tex]\[ A_{\text{path}} = 124.62 \text{ square yards} - 49.82 \text{ square yards} \][/tex]
[tex]\[ A_{\text{path}} = 74.8 \text{ square yards} \][/tex].
Which is the graph of f(x) = (x – 1)(x + 4)?
Answer:
The fourth graph (last graph)
Step-by-step explanation:
Remember that the zeros of a function are the x-intercepts of the graph. To find the zeros we just need to set the function equal to zero and solve for x:
[tex]f(x)=(x-1)(x+4)[/tex]
[tex](x-1)(x+4)=0[/tex]
[tex]x-1=0,x+4=0[/tex]
[tex]x=1,x=-4[/tex]
Now we know that the graph or our function intersects the x-axis at x = 1 and x = -4.
Since both x values inside the parenthesis are positive, our parabola is opening upwards.
The only graph opening upwards whose x-intercepts are x = 1 and x = -4 is the fourth one.
We can conclude that the graph of [tex]f(x)=(x-1)(x+4)[/tex] is the fourth one.
ANSWER
See attachment.
EXPLANATION
The given function is
f(x) = (x – 1)(x + 4).
This parabola will open upwards because the leading coefficient is positive.
The x-intercepts can be found by equating the function to zero.
[tex](x - 1)(x + 4) = 0[/tex]
By the zero product property;
[tex]x - 1 = 0 \: or \: x + 4 = 0[/tex]
This implies that,
[tex]x = 1 \: or \: x = - 4[/tex]
The graph that touches the x-axis at -4 and 1, and opens upwards is the last graph.
The correct choice is D.
What is the volume of the cone below?
ANSWER
B.
[tex]112\pi \: {units}^{3} [/tex]
EXPLANATION
The volume of a cone is calculated using the formula:
[tex]Volume = \frac{1}{3} \pi {r}^{2}h[/tex]
where r=4 units is the base radius of the cone.
and h=21 units is the vertical height of the cone.
We plug in the values to get;
[tex]Volume = \frac{1}{3} \times \pi \times {4}^{2} \times 21[/tex]
[tex]Volume = 112\pi \: {units}^{3} [/tex]
Answer:
The correct answer is option B. 112π units ³
Step-by-step explanation:
Formula
Volume of cone = (πr²h)/3
Where r - Radius of cone and
h - Height of cone
To find the volume of cone
Here radius r = 4 units
Height h = 21 units
Volume = (πr²h)/3
= (π * 4² * 21)/3
= 112π units ²
Therefore the correct answer is option B. 112π units ³
write an equation in slope-intercept form for the line with slope -2 and y-intercept 5. then graph the line.
equation: y = ?
Answer:
y = -2x + 5.
Step-by-step explanation:
The general form is y = mx + b where m = the slope and b = the y-intercept.
So here m = -2 and b = 5 so our equation is:
y = -2x + 5.
When solving the equation log7 (x+1) + log7x = log7 12 a student arrives at a verifiable solution and an extraneous solution. The value of the extraneous solution is
3
-4
-3
5.5
Answer:
[tex]-4[/tex]
Step-by-step explanation:
The given logarithmic equation is:
[tex]\log_7(x+1)+\log_7x=\log_712[/tex]
Recall and apply product rule of logarithms.
[tex]\log_aM+\log_aN=\log_aMN[/tex]
We apply this property to the left side of the equation to get;
[tex]\log_7x(x+1)=\log_712[/tex]
We take the antilogarithm of both sides to get:
[tex]x(x+1)=12[/tex]
We expand to obtain:
[tex]x^2+x=12[/tex]
We rewrite in the standard quadratic form:
[tex]x^2+x-12=0[/tex]
We factor to obtain:
[tex](x-3)(x+4)=0[/tex]
Either [tex](x-3)=0[/tex] or [tex](x+4)=0[/tex]
Either [tex]x=3[/tex] or [tex]x=-4[/tex]
But the domain is[tex]x\:>\:0[/tex].
Hence [tex]x=-4[/tex] is an extraneous solution.
A cylinder has a diameter of 22 cm and a height of 9 cm. Identify the volume of the cylinder to the nearest tenth. HELP PLEASE!!
Answer: 3421.19
Step-by-step explanation:
look up cylinder formula and r= radius which is just the diameter cut in half
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 3421.1944 cm³.
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.
Given the diameter of the cylinder is 22 cm, therefore, the radius of the cylinder is 11cm, Also, given the height of the cylinder is 9 cm.
The volume of the cylinder = πR² × H
= π × (11cm)² × 9cm
= 1089π cm³
= 3421.1944 cm³
Hence, the volume of the cylinder is 3421.1944 cm³.
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Adult tickets for the game cost $4 each and student tickets cost $3 each. A total of 105 tickets worth $380 were sold. How many student tickets were sold?
Answer:
There were 40 student tickets sold.
Step-by-step explanation:
First I set up equations to represent this situation.
4x+3y=380
x+y=105
x represents the adult tickets and y represents the student tickets.
I can solve this with the elimination method. I want to cancel out the x so I will multiply every term in equation 2 by -4.
4x+3y=380
-4x-4y=-420
Now I combine like terms.
-y=-40
I can divide the negative one from both sides.
y=40
40 Tickets sold.
Thank me later.
Miguel has started training for a race. The first time he trains, he runs 0.5 mile. Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time. What arithmetic series represents the total distance Miguel has run after he has trained n times?
Answer:
[tex]0.4n+0.1n^2\ miles[/tex]
Step-by-step explanation:
The first time he trains, he runs 0.5 mile, then the first term of the arithmetic sequence is [tex]a_1=0.5.[/tex]
Each subsequent time he trains, he runs 0.2 mile farther than he did the previous time, then the difference of the arithmetic sequence is [tex]d=0.2.[/tex]
The nth term of the arithmetic sequence can be found using formula
[tex]a_n=a_1+(n-1)d,[/tex]
hence
[tex]a_n=0.5+0.2(n-1)\\ \\a_n=0.5+0.2n-0.2\\ \\a_n=0.3+0.2n.[/tex]
The total distance after Miguel has trained n times can be found using formula
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n,[/tex]
thus, the total distance is
[tex]S_n=\dfrac{0.5+0.3+0.2n}{2}\cdot n=\dfrac{0.8+0.2n}{2}\cdot n=(0.4+0.1n)n=0.4n+0.1n^2.[/tex]
Answer:
First answer is C. (0.3+0.2K)
Second one is 15 Times
Step-by-step explanation:
Answer on EDG hope it helps :)
Three consecutive integers have a sum of 42. Find the integers.
100
Clear
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Answer:
The three integers are 13,14,15
Step-by-step explanation:
Let x be the first integer
x+1 be the second integer
x+2 be the third integer
The sum of the three integers is 42
x+ (x+1) + (x+2) = 42
Combine like terms
3x+3 = 42
Subtract 3 from each side
3x+3-3 = 42-3
3x= 39
Divide by 3
3x/3 = 39/3
x = 13
x+1 = 14
x+2 = 15
The three integers are 13,14,15
A woman invests $5800 in an account that pays 6% interest per year, compounded continuously.
a) What is the amount after 2 years? (Round your answer to the nearest cent.)
b) How long will it take for the amount to be $8000? (Round your answer to two decimal places.)
a) The amount after 2 years with continuous compounding is approximately $6539.48.
b) It will take approximately 2.32 years for the amount to reach $8000 with continuous compounding.
a) To calculate the amount after 2 years with continuous compounding, you can use the formula:
[tex]A = P \times e^{rt}[/tex]
Where:
A = the amount after time 't'
P = the principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = the interest rate (as a decimal)
t = the time in years
Given that P = $5800, r = 6% (0.06 as a decimal), and t = 2 years, we can now calculate the amount (A):
[tex]A = 5800 \times e^{0.06 \times 2}[/tex]
[tex]A=5800 \times e^{0.12}[/tex]
[tex]A=5800 \times 1.1275[/tex]
A=6539.48
Hence, the amount after 2 years is approximately $6539.48.
b) To find how long it takes for the amount to be $8000, we need to solve for 't' in the formula:
[tex]A = P \times e^{rt}[/tex]
Given that A = $8000 and P = $5800, we can rearrange the formula:
[tex]e^{rt}=\frac{A}{P}[/tex]
[tex]e^{0.06t}=\frac{8000}{5800}[/tex]
Take logarithms on both sides:
[tex]0.006t=log(\frac{8000}{5800})[/tex]
[tex]0.006t=0.139[/tex]
t=0.139/0.06
t=2.327
Hence, it takes 2.32 years for the amount to be $8000.
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After 2 years, the investment grows to approximately $6498.78. It will take around 5.37 years for the investment to grow to $8000.
Explanation:We can use the formula for continuously compounded interest, which is A = Pe^(rt), where P is the principal amount ($5800), r is the interest rate (6% or 0.06), t is the time, and e is the mathematical constant approximated as 2.71828.
a) To find the amount after 2 years, sub in $5800 for P, 0.06 for r, and 2 for t to get: A = $5800 * e^(0.06*2). Evaluating this gives approximately $6498.78.
b) To find out when the amount will be $8000, we set A to $8000 and solve for t, getting: t = ln($8000 / $5800) / 0.06. Evaluating this gives approximately 5.37 years.
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math help !! will mark brainliest
Answer:
y = 2 x - 1
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
When x = 1 , y= 1
x = 2 , y=3
At a competition with 5 runners, 5 medals are awarded for first place through
fifth place. Each medal is different. How many ways are there to award the
medals?
Decide if the situation involves a permutation or a combination, and then find
the number of ways to award the medals.
Answer: Permutation; number of ways = 120
Step-by-step explanation:
Answer with explanation:
Number of runner= 5
Number of Distinct Medal = 5
First Medal can be Awarded in 5 ways, second Medal can be awarded in 4 ways and third Medal can be awarded in 3 ways , fourth medal can be awarded in 2 ways and fifth Medal can be awarded in one way.
So, total number of ways =5 × 4×3×2×1=120 way
⇒We will use the concept of Permutation as there are five distinct medal and five different runners
So, Five distinct places can be filled in 5! or [tex]_{5}^{5}\textrm{P}[/tex] ways as order of arrangement is Important because any of the five candidates can win first second, third , fourth or fifth Prize.
= 5!=5×4×3×2×1=120 ways
Because, n!=n×(n-1)×(n-2)×........1.
Can a translation and a reflection map QRS to TUV? Explain why or why not. No, the triangles are not congruent. Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV. No, the triangles are obtuse. Yes, a translation mapping vertex S to vertex T and a reflection across the line containing RS will map △QRS to △TUV.
Answer:
The answer is B
Step-by-step explanation:
just took the answer on e2020
Answer:
B:
Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map △QRS to △TUV.
You were recently hired by a company and will recieve a starting salary of $45,000 per year. You will receive a $2,500 raise each year you are with the company. What will your salary be in your 8th year with the company?
Answer:
Your salary will be $62,500.
Step-by-step explanation:
This is an arithmetic sequence with first term $45,000 and common difference $2,500.
The appropriate formula is a(n) = a(1) + (n-1)d, where a(1) is the first term, n is a counter and d is the common difference.
In this particular case, a(8) = $45,000 + (8-1)($2,500) = $62,500
Your salary will be $62,500.
A function assigns the values. Your salary after completing the 8th year within the company will be $62,500.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that the starting salary will be $45,000 while the salary will increase every year by $2,500. Therefore, the function that can represent the salary after (n-1) years can be written as,
y = $45,000 + $2,500(n-1)
Now, the salary after 8th year will be,
y = $45,000 + $2,500(n-1)
y = $45,000 + $2,500(8-1)
y = $62,500
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calculate the value of A
Answer:
Second Option
[tex]a=1.46[/tex]
Step-by-step explanation:
The triangle of the figure is a straight triangle.
We know the length of the hypotenuse, h = 2, and we know the angle A = 43°. We need to find the length a. Side a is the side adjacent to the 43° angle
By definition we know that
[tex]cosx = \frac{adjacent}{hypotenuse}[/tex]
Then
adjacent = a
hypotenuse =2
x =43°
[tex]cos(43\°) = \frac{a}{2}[/tex]
[tex]a= 2cos(43\°)[/tex]
[tex]a= 1.46[/tex]
Use substitution to solve the system of equations. 2x+4y=8 3x-5y=1
ANSWER
The solution is (2,1)
EXPLANATION
The given equations are:
2x+4y=8...(1)
3x-5y=1...(2)
We make x the subject in the first equation to get:
2x=8-4y
This means that,
x=4-2y...(3)
Put equation (3) into equation (2)
3(4-2y)-5y=1
Expand:
12-6y-5y=1
-6y-5y=1-12
-11y=-11
y=1
Put y=1 into equation (3).
x=4-2(1)=2
The solution is (2,1)
50 POINTS PLEASE HELP!!
Which values of a, b, and c represent the answer in simplest form?
5/8 divided by 3/8= a b/c
a. a=1, b=3, c=2
b. a=1, b=40, c=24
c. a=1, b= 16, c=24
d. a=1. b=2, c=3
Answer:
d. a=1. b=2, c=3
multiply by the Reciprocal.
Answer:
D
Step-by-step explanation:
(5/8) / (3/8)
(5/8) * (8/3)
5/3
1 ⅔
a = 1, b = 2, c = 3
Answer D.
Majel is making batches of trail mix. Each batch uses 3/4 cup of granola. How many batches of trail mix can Majel make from 6 1/2 cups of granola
Answer: 8 2/3
Step-by-step explanation:
SOMEONE
HELP PLEASE!!
Answer:
it is the third one (from left to right)
Step-by-step explanation:
no explation
Misty has the choice of taking out a 25-year loan for $105,000 at 3.8% interest, compounded monthly, or the same loan at 20 years for a higher monthly payment. If she would pay a total of $57,810 in interest on the 25-year loan, how much in total would she pay in interest on the 20-year loan?
Without more information, we cannot give a specific numerical answer for the total interest on a 20-year loan. As a rule, total interest paid will be less on a shorter loan, despite higher monthly payments.
Explanation:The question is asking how much total interest would Misty pay on a 20-year loan, given she knows the total interest paid on a 25-year loan to be $57,810. We're not given enough information to provide a specific numerical answer for this - the loan interest for a 20-year loan and a 25-year loan involve different payment schedules and amounts - so we can't directly compare or convert the total interest paid.
However, generally speaking, the total interest paid over a shorter loan term (i.e. 20 years) is expected to be less than that of a longer term (i.e. 25 years), assuming all else (loan amount, interest rate) remains equal - this is because the principal balance is being paid down more rapidly, leaving less time for interest to accrue. The trade-off is that monthly payments would be higher on the shorter term loan.
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The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas. True or false
Answer:
True
Step-by-step explanation:
The area of a regular polygon is found by multiplying 1/2 times the apothem times the perimeter. The area for a single triangle is 1/2 times the height (which is the same as the apothem of a regular polygon) times the base (which is one of the sides of the regular polygon which you are multiplying by to find the perimeter of the polygon).
Answer:
The given statement is true.
Step-by-step explanation:
The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas.
This is true.
Breaking down in 7 triangles and adding separately the areas of these triangles, will give the complete area of the heptagon. We can also find the area of one triangle and multiply that by 7 to get the same result.
Please help me out with this
Answer:
11.6 cm²
Step-by-step explanation:
The area (A) of the shaded region is
A = area of sector - area of triangle
area of sector = area of circle × fraction of circle
= π × 9.28² ×[tex]\frac{68.9}{360}[/tex] ≈ 51.78 cm²
area of triangle = [tex]\frac{1}{2}[/tex] × 9.28 × 9.28 × sin68.9°
= 0.5 × 9.28² × sin68.9 ≈ 40.17 cm²
Area of shaded region = 51.78 - 40.17 ≈ 11.6 cm²
An online service charges $3 for each downloaded movie, plus a monthly fee of $6.50. Which function represents this situation?
y = 3x - 6.50
y = 6.50x - 3
y = 3x + 6.50
y = 6.50x + 3
ANSWER
y = 3x + 6.50
EXPLANATION
The $3 for each downloaded movie is the unit rate of change.
This is represent the slope of the linear function that models this situation.
The monthly fee of monthly fee of $6.50 the constant rate.
It represents the y-intercept of the function.
The linear function is given by
[tex]y = mx + b[/tex]
The correct choice is y = 3x + 6.50
the answer would be C. y = 3x + 6.50, for every movie you buy (which is x), they would be 3$. therefore it would be 3x, and the monthly fee would just be added with that. :P
Tina bought a t shirt and sandals the total cost was 41.50. The t shirt cost 8.95. The equation 8.95 + c = 41.50 can be used to find the cost c in dollars of the sandals how much did the sandals cost
Answer:
sandals costed $32.55
Step-by-step explanation:
Final answer:
To find the cost of the sandals, subtract the cost of the T-shirt from the total cost. The equation 8.95 + c = 41.50 leads to c = 32.55, meaning the sandals cost $32.55.
Explanation:
The question asks us to find the cost of sandals that Tina bought, given the total cost of a T-shirt and the sandals combined, and the cost of the T-shirt alone. To solve for the cost c of the sandals, we start with the equation 8.95 + c = 41.50. We then isolate c by subtracting 8.95 from both sides of the equation:
c = 41.50 - 8.95
c = 32.55
Therefore, the cost of the sandals was $32.55.
math question! please help!
Answer:
the correct choice is marked
Step-by-step explanation:
The red line has intercept -3 and slope 1/3, so is ...
y = 1/3x -3
The blue line has intercept +1 and slope -1, so is ...
y = -x +1
The graph solves this system of equations, which can also be written as the single equation ...
y = y
1/3x -3 = -x +1
Use the function below to find F(4)
[tex]F(x) = 5 *(\frac{1}{2})^x[/tex]
[tex]
f(4)=5\times(\frac{1}{2})^4 \\
f(4)=\frac{5\times1^4}{2^4} \\
f(4)=\boxed{\frac{5}{16}}
[/tex]
Hope this helps.
Brainliest would be great.
For this case we have a function of the form[tex]y = f (x)[/tex]
Where:
[tex]f (x) = 5 * (\frac {1} {2}) ^ x[/tex]
We must find the value of the function when x = 4, that is, f (4):
Substituting we have:
[tex]f (x) = 5 * (\frac {1} {2}) ^ 4\\f (x) = 5 * \frac {1} {2} * \frac {1} {2} * \frac {1} {2} * \frac {1} {2}\\f (x) = 5 * \frac {1} {16}\\f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]
ANswer:
[tex]f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]
Please help with question 5!
Answer:
68
Step-by-step explanation:
[tex]a_2=2a_1+4=2\cdot 5+4=14\\\\a_3=2a_2+4=2\cdot 14+4=32\\\\a_4=2\cdot 32+4=68[/tex]
a₄ = 68
_____
The explicit formula is
an = 9·2^(n-1) -4
Can someone explain this?
The answer is:
The missing step is the step shown in the last option:
D. [tex]324=0.042x+16[/tex]
Why?To find which is the missing step, we need to remember that to cancel a square root, we need to elevate it, so:
Starting from the last step before the missing step, we have:
[tex]-18=-\sqrt{0.042x+16}[/tex]
In order to calculate the value of the variable (x) we need to square both sides of the equation, since squaring a root will cancel the root.
We must remember the following properties:
[tex]\sqrt{a^{m} }=a^{\frac{m}{2}}\\\\(a^{b})^{c}=a^{b*c}[/tex]
Now, finding the missing step, we need to find what to do in order to get the expression of the following step.
So, squaring both sides of the equation in order to cancel the square root and isolate the variable, we have:
[tex]-18=-\sqrt{0.042x+16}\\\\(-18)^{2} =(-\sqrt{0.042x+16})^{2} \\324=0.042x+16\\324-16=0.042x\\\\x=\frac{304}{0.042}=7333[/tex]
Hence, we found the the missing step is:
D. [tex]324=0.042x+16[/tex]
Have a nice day!
The residuals for data set X and data set Y were calculated and plotted on separate residual plots. If the residuals for data set X do not form a pattern and the residuals for data set Y form a pattern, what can be concluded?
A. Data set X is not linear, and data set Y is not linear.
B. Data set X is not linear, and data set Y is linear.
C. Data set X is linear, and data set Y is linear.
D. Data set X is linear, and data set Y is not linear.
Answer:
B. Data set X is not linear, and data set Y is linear.
Step-by-step explanation:
We assume here that "form a pattern" means "roughly forms a line"... because a pattern doesn't necessarily equal a line, it would be a curve that would easily be interpreted too, but it wouldn't be linear.
Since you cannot form a pattern, and based on your choices for answer, we have have to say that data set X is NOT linear.
On the opposite, since the data set Y produces a pattern, it has to be linear.
So, X = NOT linear, Y = linear.
Answer:
(Data set x is linear, and data set y is not linear.) This is the correct answer 100%...
When i put the answer in from the other person which was (x is not linear, and y is linear) it said incorrect and gave me this answer x is linear, and y is not linear. So be careful what you put down.
Step-by-step explanation:
Jacob will pay a monthly payment of $650.12 on a fixed rate mortgage over 20 years. What is the total principal and interest for the life of this mortgage rounded to the nearest dollar? I think maybe D.
A. $234,043
B. $13,002
C. $195,036
D. $156,029
I believe the answer is d. 156,029
I think the answer is D
Name the quadrant in which tanθ and secθ are positive.
ANSWER
Quadrant I
EXPLANATION
In the first quadrant all the trigonometric ratios are positive.
This implies that,both tanθ and secθ are positive in the first quadrant.
No two trigonometric ratios are positive in any other quadrant apart from the first quadrant.
Answer:
qaud I
Step-by-step explanation: