Answer:
total area of the garden and walkway = 2a² + 21a + 54
Step-by-step explanation:
The walkway surrounds the rectangular garden. The width of the garden is 9 ft and the length is 12 ft. Since the width of the walkway around the garden is the same on every side let us use a to represent the width around the garden.
The garden is rectangular and the width of the walkway around the garden is uniform. The width added on both end of the width of the rectangle will be 2a while the width added to the both length of the rectangle will be 2a also.
Therefore
total area of the garden and walkway = length × width
length of garden and the walkway = 2a + 12
width of garden and the walkway = 2a + 9
total area of the garden and walkway = (2a + 12)(2a + 9)
total area of the garden and walkway = 4a² + 18a + 24a + 108
total area of the garden and walkway = 4a² + 42a + 108
divide through by 2
total area of the garden and walkway = 2a² + 21a + 54
A recipe needs 4/5 cups of butter for every 2 cups of flour. If you plan to use 3 cups of flour, how much butter will you need?
Answer:
1 1/5 cups of butter
Step-by-step explanation:
4/5=2
=3
4/5 x 3=12/5
12/5 / 2
12/5 x 1/2=1 1/5
Solve for
theta in the interval 0 ≤ theta≤ 2 pi
cos theta sin theta − 1/2 sin theta=0
Answer:
< theta international
Which of the following is equivalent to 7-2( x + 2) <-4 - 3(1 – x)?
(A) -5 x < -10
(B) - X<-16
(C) -2x <-17
(D) 6x<-9
what is the area of a sector created by a circle with a radius of 4cm and a 40 central angle
Answer:
5.59 cm
Step-by-step explanation:
I had set up a proportion. The proportion is below.
360° 50.27
------- = ----------
40° ? (What you're trying to figure out)
So what I did was 50.27 times 40 which equals: 5.58555556, so I rounded it to 5.59 so that's your answer!
I hope that's helpful :D
When 240 sixth-grade students were polled, results showed that 96 students were dissatisfied with the music played at the school dance. What percentage of the sixth-grade students does this represent? Use at least 2 strategies.
Answer:
40%
Step-by-step explanation:
one strategie is doing proportions
96/240= ?/100
simplify 96/240= 2/5
so 2/5=?/100
multiply 100 by 2
then divide it by 5
another strategie is putting it into a decimal and percent
96/240= 2/5
in decimal is 0.40
move the decimal twice to the right and you get 40%
Michel started to drive from New York to Washington, DC, which is 120 miles away, at 7:00 AM. For the first hour and a half of her trip, Michel was driving at a speed of 50 mph. What was her average speed during the second part of the trip, if she reached Washington at 10:00 AM?
Answer:
30 mph
Step-by-step explanation:
Identify the terms and the like terms in this expression.
7 + a – 2 + 3a + b^2
Which statements are true? Check all that apply.
a. The expression contains seven terms.
b. The terms in the expression are 7, a, 2, 3a, b2.
c. Constants are like terms.
d. 2 and b2 are like terms because they both contain the number 2.
e.a and 3a are like terms.
f. a, 3a, and b2 contain variables, so they are like terms.
Answer:
B, C, E
Step-by-step explanation:
I took the test and I got it right
Answer: B C E
Step-by-step explanation: Edge 2020-WAiT! It’s not 2020 any MORE! Anyways edge 2021
If we draw a ball from an urn containing 10 numbered balls, with seven red balls that are numbered 1, 2, 3, 4, 5, 6, 7 and three that are green and are numbered 8, 9, 10, what is the probability of drawing a ball that is red and even?
a. 2/5
b. 3/10
c. 1/2
d. 4/7
Answer:
b
Step-by-step explanation:
Angela and Tyler are selling tickets for a charity football game. Students will get a discount for the game. Angela sells 6 adult ticket and 10 student ticket for $122. Tyler sells 11 adult tickets and 5 student tickets for a total of $157. What is the of an adult ticket and what is the price of a student ticket?
A, Define your varibles and write a system of equations that represents the ticket sales for both Angela and Tyler.
let x=
Let y=
system of equation:
B' Solve system of equation
c' Write answer using a complete sentence.
Answer:
Step-by-step explanation:
Let’s say that the price of an adult ticket is x and a student ticket is y.
we know that 6 adult tickets (6x) and 10 student tickets (10y) equal 122, so 6x+10y=122. Then, 11x+5y=157
6x+10y=122
11x+5y=157
Multiply the first equation by -1/2 and add it to the second to cancel out the y
8x=96
x=12
Plug this back in to equation 2 to find y
132+5y=157
y=5
Checking this with the first equation, it all works out.
The price of an adult ticket for a charity football game is $12, while the price for a student ticket for the same game is $5
Which equation in rectangular form describes the parametric equations x=5-3cost and y=4+2sint?
A. (x+5)^2/9+(y+4)^2/4=1
B. (y+4)^2/2-(x+5)^2/3=1
C. (y-4)^2/2-(x-5)^2/3=1
D. (x-5)^2/9+(y-4)^2/4=1
Answer:
D. (-x+5)^2/9+(y-4)^2/4=1 (I assume there was a mistype)
Step-by-step explanation:
The first step is isolating the sine and cosine functions.
x=5-3cos(t)
x + 3cos(t) = 5
3cos(t) = 5 - x
cos(t) = (5 - x)/3
y=4+2sin(t)
y - 4 = 2sin(t)
(y - 4)/2 = sin(t)
Then, square at both sides of the equal sign
cos²(t) = (5 - x)²/3² = (5 - x)²/9
sin²(t) = (y - 4)²/2² = (y - 4)²/4
Recall the trigonometric identity and replace.
cos²(t) + sin²(t) = 1
(5 - x)²/9 + (y - 4)²/4 = 1
Which expression should you simplify to find the 90% confidence interval,
given a sample of 64 people with a sample proportion of 0.55?
Step-by-step explanation:
CI = p ± z √(pq/n)
For 90% confidence, z = 1.645.
CI = 0.55 ± 1.645√(0.55 × 0.45 / 64)
The expression to find the 90% confidence interval is
[tex]CI = 0.55 + 1.645 \sqrt{\frac{0.55 ( 0.45)}{64} }[/tex]
What is confidence interval?A confidence interval is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.
CI z
0.70 1.04
0.75 1.15
0.80 1.28
0.85 1.44
0.90 1.645
0.92 1.75
0.95 1.96
0.96 2.05
0.98 2.33
0.99 2.58
According to the question
Data of people = 64
Data proportion (P) = 0.55
The 90% confidence interval
therefore, [tex]z_{c}[/tex] = 1.645
CI = P± [tex]z \sqrt{\frac{P ( 1-P}{N} }[/tex]
substituting the value
[tex]CI = 0.55 + 1.645 \sqrt{\frac{0.55 ( 0.45)}{64} }[/tex]
CI = 0.5563
Hence, expression to find the 90% confidence interval is
[tex]CI = 0.55 + 1.645 \sqrt{\frac{0.55 ( 0.45)}{64} }[/tex]
To know more about confidence interval here:
https://brainly.com/question/24131141
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a new school has a teacher to student ratio is 2:15. the school has 42 teachers. how many students are there in the school?
Answer:
315
Step-by-step explanation:
42÷2 = 21
2×21 = 42
So, 15×21 = 315
315÷21 = 15
Answer:
315
Step-by-step explanation:
42÷2 = 21
2×21 = 42
So, 15×21 = 315
315÷21 = 15
Help
Please!!!!!!!!!
Answer:
6 s^9t^3
...............
Use the elimination method to solve the system of equations. Choose the
correct ordered pair.
x-3y = -19
2x+y=-3
A. (-2, 1)
B. (-4,5)
C. (4, -11)
D. (-1,1)
SUBMIT
Answer:
x=-4,y=5
Step-by-step explanation:
Answer:
B (-4,5)
Step-by-step explanation:
x-3y=-19
2x+y=-3
this is how I'll start it off, I'll multiple the bottom equation by 3 to have the y-value become the reciprocal (opposite) of the top equation.
now it's:
x-3y=-19
6x+3y=-9
now add/subtract
7x=-28
divide 7 from both sides
x=-4
now plug -4 into the equations to get y
-4-3y=-19
add 4 to both sides to get rid of -4
-3y=-15
divide -3 on both sides
y=5
now to double check, do the other equation
2(-4)+y=-3
-8+y=-3
add 8 to both sides to get rid of -8
y=5
now to check the answer, plug in x=-4 and y=5 into the equations
-4-3(5)=-19
-4-15=-19
2(-4)+5=-3
-8+5=-3
If 3n – 2 = 10, then n = _______.
Answer:
n = 4
Step-by-step explanation:
[tex]3n-2=10\\3n=10+2\\3n=12\\n=12/3\\n=4[/tex]
I hope I helped you! Please mark me brainiest if I am correct. Thanks!
Answer:
n=4
Step-by-step explanation:
What do the variables in this problem stand for V=Bh
V=
B=
h=
Please help
Please I need help with my geometry math assignment with 13C and is Almost soon to due and I been struggling and needing help on it I try my best and don’t work out for me so I will mark your guys brainlist
Answer: y = 2x + 2
Step-by-step explanation:
To find the slope of a line perpendicular to another line, you take the slope of the other line and flip it (find the negative reciprocal) and make it negative.
In this case, -1/2 would become 2. 2 is now the slope of the line perpendicular to the other line.
Since the line passes through (1, 4), we can plug the point in - the line will be
y = 2x + 2.
Answer:
y=2x+2.
Step-by-step explanation:
Honestly the perpendicular flipping didn't make sense, but somehow google thought so, so ill leave it at this, if you need more help, just message me.
For what values of k the relation R:{(k2 , 5), (3k, 6)} is not a function?
Explanation:
If you have repeated x values, then you wont have a function. For example, the points (1,5) and (1,6) mean we don't have a function since the input x = 1 leads to multiple outputs y = 5 and y = 6 simultaneously. For a function to be possible, we must have any input lead to exactly one output only.
What we do is set the x coordinates (k^2 and 3k) equal to each other and solve for k
k^2 = 3k
k^2-3k = 0
k(k-3) = 0 .... factoring
k = 0 or k-3 = 0 .... zero product property
k = 0 or k = 3
If k = 0, then (k^2,5) becomes (0,5). Also, (3k,6) becomes (0,6). The two points (0,5) and (0,6) mean the graph fails the vertical line test.
Similarly, if k = 3, then (k^2,5) becomes (9,5) and (3k,6) = (9,6). Another vertical line test failure happens here to show we don't have a function.
Im not sure about the answer
Answer:
D. 5:7 and 10:14
Step-by-step explanation:
25:35=5:7
5x2=10
7x2=14
Can someone answer 32 points
Answer:
a= 3/4
Step-by-step explanation:
2/3 x 3/4- 1/6 = 1/3
pls help will mark as brainliest
Answer:
C or [tex]y=\frac{1}{4}^{x}[/tex]
Step-by-step explanation:
when x is 0 y is 1 and every positive number to the zeroth power is 1
so It can be A or C
but the value of y goes down when x goes up so its exponential decay or less than 1 so 1/4<1 So
C or [tex]y=\frac{1}{4}^{x}[/tex]
Identify the solutions to the quadratic equation
x2 + 4x-21 = 0
Check all that apply
O A. x= 3
B. X= -7
O C. x = 21
O D. x= -5
O E. x= 4
Answer:
Step-by-step explanation:
Solving quadratics is easy. With no coefficient to the x^2, we can go right to finding factors. We want two numbers that multiply to -21, and add to 4. Our numbers are 7, and -3. Now, we move the numbers around to be (x-3) and (x+7). We know that these both equal 0, so we can do basic algebra to solve for x. We can subtract 7 to the other side to just get x, and add 3 over because it is subtracted by x. This leaves us with our answers:
x = -7, x = 3
The dimensions of a rectangle are x+4 and 3x-1. Write an expression to represent the area of the rectangle.
Answer:
9x^4 - 6x^3 + 97x2 - 88x + 16
Step-by-step explanation:
so (x + 4)(x + 4) = x^2 + 8x + 16 is the total length of the rectangle, and
(3x - 1)(3x - 1) = 9x^2 - 6x + 1, if you multiply each other, because Area = length times width, then you get the area.
(9x^2 - 6x + 1)(x^2 + 8x + 16) = 9x^4 + 72x^2 + 144x^2 - 6x^3 - 48x^2 - 96x + x^2 + 8x + 16, and then you add them all together = 9x^4 - 6x^3 + 98x^2 - 96x + 8x + 16 = 9x^4 - 6x^3 + 97x2 - 88x + 16
39 less than the product of a number and 13 is 39
Answer:
13n - 39 = 39
Step-by-step explanation:
Let the number be n. Then we have 13n - 39 = 39
Evaluate y=(1/5)x
when x=- 3
Answer:
125y
hope this helps
Answer:
Y = 125
Step-by-step explanation:
which of the following is equal to the square root of -5
Answer:
√5 i
Step-by-step explanation:
√-5
√5*√-1
√-1=i
√5*i
√5 i
Solve –3d + 5 = 14.
–57
12
–27
–3
Answer:
d = -3
Step-by-step explanation:
–3d + 5 = 14.
Subtract 5 from each side
–3d + 5-5 = 14-5
-3d = 9
Divide each side by -3
-3d/ -3 = 9/-3
d = -3
Answer:
[tex]d = - 3[/tex]
last answer is correct
Step-by-step explanation:
[tex] - 3d + 5 = 14 \\ - 3d = 14 - 5 \\ - 3d = 9 \\ \frac{ - 3d}{ - 3} = \frac{9}{ - 3} \\ d = - 3[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
gerald accepted a job as jazz pianist after being offered a $425 signing bonus l, if he makes $24 an hour, which equation models gerald's total pay y, in dollars, as it relates to the number of hours x that he works ?
Answer:
425+24x=y
Step-by-step explanation:
Answer: y=425x + 24
Step-by-step explanation: :PP
Can anyone help? I will mark you as brainliest!
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First calculate the area of the field using this equation:
area = (a+b)/2 x h
Substitute the values in:
area = (210 + 190)/2 x 250
area = 50000 m^2
Calculate how many hectares this is:
50000/10000 = 5
This is 5 hectares
Multiply this by the number of kg per hectare
5 x 7200 = 36000
It would produce 36000 kg
Have A Nice Day ❤
Stay Brainly! ヅ
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A line has a slope of -3 and a y-intercept of 3.
6
4 +
3
1
-5 -4 -3 -2 -1
-1,
1
2
3
4 5
Answer:
y = -3x + 3
Step-by-step explanation:
If ... A line has a slope of -3 and a y-intercept of 3, then the equation of that line is y = mx + b => y = -3x + 3. You don't need the table of values.