Part A
Which of the following is an expression for a in terms of x?
Part B
What is the maximum area, in square feet, for the garden if 44 feet of fencing are used?
I really need help with this question. I am doing Algebra NJSLAM practice and I’m not sure how to do this problem.
Answers
the first choice is correct
The maximum area of the rectangle will be 242 square ft. The expression for a in terms of x will be 44 - 2x. Then the correct option is C.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
If the a, b, and x are 44 ft. Then the expression for a in terms of x will be
We know that b = x
Then we have
a + b + x = 44
a + 2x = 44
a = 44 - 2x
Then the area opf the rectangle will be
Area = (44 - 2x)x
Area = 44x - 2x²
For maximum area the value of x will be 11. Then we have
Area = 44 × 11 - 2 × 11²
Area = 242 square ft
More about the square link is given below.
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Related Questions
What is the value of (–3 + 3i) + (–2 + 3i)? –5 – 6i –5 + 6i 5 + 6i 5 – 6i
Answers
Answer: Second option
[tex]-5 + 6i[/tex]
Step-by-step explanation:
The expression [tex](-3 + 3i) + (-2 + 3i)[/tex] is the sum of two complex numbers and their real part
To solve the sum you must add the real parts with the real parts and the complex numbers with the complex numbers
so, we have:
[tex]-3 + 3i -2 + 3i\\\\(-3 - 2) + (3i + 3i)\\\\-5 + (3i + 3i)\\\\-5 + 6i[/tex]
the answer is the second option
[tex]-5 + 6i[/tex]
for a field trip the school bought 67sandwiches for 6.60 each and 59 bags of chips for 3.25 each . how much did the school spend in all
Answers
Answer:663.95$
Step-by-step explanation:
Answer:
633.95
Step-by-step explanation:
Given: m∠MEJ=30°, m∠MFJ=50° , Find: Measurement of Arc KL & Measurement of Arc MJ
Answers
Answer:
Part a) The measurement of arc KL is [tex]20\°[/tex]
Part b) The measurement of arc MJ is [tex]80\°[/tex]
Step-by-step explanation:
Let
x--------> the measure of arc KL
y-------> the measure of arc MJ
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
[tex]m<MEJ=\frac{1}{2}(y-x)[/tex]
substitute the given value
[tex]30\°=\frac{1}{2}(y-x)[/tex]
[tex]60\°=(y-x)[/tex]
[tex]y=60\°+x[/tex] ------> equation A
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
[tex]m<MFJ=\frac{1}{2}(x+y)[/tex]
substitute the given value
[tex]50\°=\frac{1}{2}(x+y)[/tex]
[tex]100\°=(x+y)[/tex]
[tex]y=100\°-x[/tex] ------> equation B
Equate the equation A and B and solve for x
[tex]60\°+x=100\°-x[/tex]
[tex]2x=100\°-60\°[/tex]
[tex]x=20\°[/tex]
Find the value of y
[tex]y=100\°-20\°=80\°[/tex]
therefore
The measurement of arc KL is [tex]20\°[/tex]
The measurement of arc MJ is [tex]80\°[/tex]
In the drawer you have 8 black socks and 5 yellow socks , if you pick out a sock what is the probability that the pick out a yellow sock?
Answers
Answer:
Step-by-step explanation:
I believe the answer is 5/13 chance because 8 black socks then 5 yellow so In total there are 13 socks and the question revolves around the yellow socks so 5/13 chance. Hope it helps. :)
5/13 because there is 13 socks all together and 5 of them are yellow
What is the mode of the data?
3
5
7
8
tell me what to do bc i have 8 of them to do o3o
Answers
Answer:
5
Step-by-step explanation:
Mode means most, so it's the number you see most.
Tomás built several towers with rectangular blocks. Which formula best represents the heights of the blocks in terms of their volumes?
Answers
Answer:
Option A
V = 15h
Step-by-step explanation:
Given in the question some information regarding the heights and volume of the towers with rectangular blocks
Formula to use
Volume = Length x Width x Height30 = Length x Width (2)
Length x Width = 30/2
Length x Width = 15
Formula best represents the heights of the blocks in terms of their volumes
V = 15h
Answer:
The correct answer is option A. 15h
Step-by-step explanation:
From the figure we can see that a table shows the relationship between heights and volume of rectangular blocks.
Heights Volume
2 15
3 45
4 60
10 150
To find the formula in terms of heights
If height = 2 then volume = 30 = 2 * 15
If height = 3 then volume = 45 = 3 * 15
If height is 'h' then volume = 15 * h = 15h
The correct answer is option A. 15h
Tim Tradesman pays $2,000 annually for $150,000 worth of life insurance. Answer the following questions. a. At the end of 10 years, how much will Tim have paid in premiums? b. At the end of 10 years, what will the cash value of his policy be? c. What will the ratio of cash value to premiums paid be (as a percent)?
Answers
____________________________________________________
Explanation for question A:
We are trying to found the amount of money he payed after 10 years.
He pays an annual (yearly) of $2,000, so we would just multiply 2,000 by 10, since we are trying to find the amount he point in 10 years, in which he pays $2,000 a year.
[tex]2000*10=20000[/tex]
Answer for Question A: Tim Tradesman paid $20,000 in premiums at the end of 10 years.
____________________________________________________
Explanation for question B:
In question B, we are trying to find the cash value of the policy at the end of 10 years.
To find the cash value at the end of 10 years, we would get the units of life insurance and multiply it by the cash value per unit
There would be 150 units of life insurance.
So we multiply:
[tex]150*89=13350[/tex]
Answer for Question B: The cash value of his policy will be $13,350 at the end of 10 years.
____________________________________________________
Explanation for question C:
In question C, we are trying to find the ratio of cash value to premiums paid.
Our cash value is 13,350 and we paid 20,000.
When you subtract 20,000 and 13,350, you would get 6,650.
[tex]20000-13350=6650[/tex]
Then when you add 20,000 and 13,350, you would get 33,350.
[tex]20000+13350=33350[/tex]
When you subtract 6,650 from 33,350, you would get 26,700
[tex]33350-6650=26700[/tex]
26,700 is 66.75% of 33,350.
Answer for Question c: The ratio as a percent for the cash value to premiums paid is 66.75%
____________________________________________________
3 to the zero power is what
Answers
Answer:
1
Step-by-step explanation:
Any number to the 0 power will always be 1.
Hope this helps ya out fam!
Welcome to Brainly btw!
~LoCoCoCo
Answer:
The answer should be 1
Step-by-step explanation:
food bill before tax:$45 sales tax:6.8% tip:24%
Answers
Answer: 58.86
Step-by-step explanation:
45(.068)= 3.06
3.06+45= 48.06
45(0.24)=10.8
48.06+10.8= 58.86
13. Write an expression that shows 17 less
than five times a number.
Answers
answer for this question is 5x-17
250 female nurses to 100 male nurses what is the ratio of male nurses to female nurses
Answers
Answer:
2:5
it may be faster to google it
Answer:
Required ratio is 2:5.
Step-by-step explanation:
Given that number of female nurses = 250
Given that number of male nurses = 100
Now we need to find about what is the ratio of male nurses to female nurses.
So we just need to divide number of male nurses by the number of female nurses. That means divide 100 by 250. We get:
[tex]\frac{male}{female}=\frac{100}{250}[/tex]
[tex]\frac{male}{female}=\frac{10}{25}[/tex]
[tex]\frac{male}{female}=\frac{2}{5}[/tex]
Hence required ratio is 2:5.
What is most likely the length of a telephone book
Answers
Answer:
its around 297mm so any choice you have there around that number choose it
Step-by-step explanation:
Dont mind what I have wrote
Answers
Answer:
n = 10
Step-by-step explanation:
[tex]\dfrac{4^8}{(4^2)^{-3}} \div 4^4 = 4^n[/tex]
[tex]\dfrac{4^8}{4^{-6}} \div 4^4 = 4^n[/tex]
[tex]4^8 \times 4^6 \div 4^4 = 4^n[/tex]
[tex]4^{(8 + 6 - 4)}= 4^n[/tex]
[tex]4^{10}= 4^n[/tex]
[tex]n = 10[/tex]
Answer:
n = 10Step-by-step explanation:
[tex]\dfrac{4^8}{(4^2)^{-3}}\div4^4=4^n\qquad\text{use}\ (a^n)^m=a^{nm}\\\\\dfrac{4^8}{4^{(2)(-3)}}}\div4^4=4^n\\\\\dfrac{4^8}{4^{-6}}\div4^4=4^n\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\4^{8-(-6)}\div4^4=4^n\\\\4^{14}\div4^4=4^n\qquad\text{use}\ a^n\div a^m=a^{n-m}\\\\4^{14-4}=4^n\\\\4^{10}=4^n\Rightarrow n=10[/tex]
Write all the factors of 16
Use commas to separate them.
Answers
Factors of 16 :
1, 2, 4, 8, 16
1,2,4,8,16
Method16 is a composite number and it is 4 squared. 16= 1x16,2x8 or 4x4. So all the factors of 16 is 1,2,4,8,16
three classes at a junior high school raised money to buy new computers
•ms moore’s class raised $249.00
•ms aguilars class raised $396.62 more than ms.moores class
•mr.barrys class raised $430.43 less than ms.augilars class
what is the total amount of money raised by all three classes
Answers
Answer:
$1109.81
Step-by-step explanation:
$249.00 +$369.62= $618.62(ms. aguilars class)
$618.92-$430.43= $188.19(mr. barry's class)
$249.00+$618.62+$188.19=$1109.81(complete answer of all 3 classes combined)
Answer:
The final amount is $1109.81
Step-by-step explanation:
In order to find the total amount, start with the know amount, which is Ms. Moore's class. Her class raised $249. Now we can use that to find the amount from Ms. Aguilar's class.
$249 + $396.62 = $645.62
Now we can use the amount from Ms. Aguilar's class to find the amount from Ms. Barry's class
$645.62 - $430.43 = $215.19
Now we can add the three amounts together to find the total amount.
$249 + $645.62 + $215.19 = $1109.81
Pls help meh!!!!!!!!
Answers
Answer:
Step-by-step explanation:
The clock on the left shows that there are 6 minutes needed to reach 4:00
The clock on the right shows that it is (5*7 + 1) = 36 minutes past 4:00
The time passed is 6 + 36 = 42 minutes.
Your scores on test in math are 89, 95 and 76. You will be taking one more test and you want your (mean) average to be 90. What will your test score have to be?
Answers
Answer:
100
Step-by-step explanation:
89+95+76=260
260+100(test score)=360
360/4=90
mark me brainiest
Suppose f(x) = x^2. what is the graph of g(x) = f(2x)?
Answers
Answer:
C
Step-by-step explanation:
Substitute 2x into the equation where x is located. G(x)= (2x)^2=4x^2. This will be a graph which has been vertically stretched has a very steep curve to it facing up. It is C.
Answer: c is the correct answer
Step-by-step explanation:
Just took it
Select the representation that does not change the location of the given point. (4, 110°)
Question 6 options:
(4, 290)°
(-4, 200)°
(4, 470)°
(-4, 470)°
Answers
Answer:
(4,470°)
Step-by-step explanation:
The representation that does not change the location of (4, 110°) in polar coordinates are all points that are coterminal with the given point.
The only point among the given options that is coterminal with (4, 110°) is (4, 470)°
The two points have the same magnitude and 470°-360°=110°.
Since 110° is coterminal with 470° and the two points have the same magnitude with the same sign, the two points represent the same location in polar coordinates.
The correct choice is (4,470°)
In the polar coordinate system, the point (4, 470°) is the representation that does not change the location of the given point (4, 110°). We obtain this by adding 360° to the given angle.
Explanation:This question is based on the concept of polar coordinates. Polar coordinates represent a point in space by specifying its distance from a reference point, usually the origin, and the angle made with the positive x-axis. In polar coordinates, (r, θ), 'r' represents the distance and 'θ' is the angle.
Given point is (4, 110°). We can notice that by adding or subtracting multiples of 360° from the angle, we are not changing the location of the point. So, if we add 360° to the 110°, we will obtain 470°. Hence, the point that represents the same location is (4, 470°).
The point (-4, 200°) represents the point in the opposite direction and the points (4, 290°) and (-4, 470°) change the angle beyond or below what is allowable without changing the point's location.
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The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of the circle circumscribed about this triangle.
Answers
ANSWER
The length of a Diameter is 3.714
EXPLANATION
The circumscribed triangle is shown in the attachment.
We use the cosine ratio to find the altitude of the isosceles triangle.
[tex] \cos(60 \degree) = \frac{altitude}{hypotenuse} [/tex]
[tex] \cos(60 \degree) = \frac{altitude}{8} [/tex]
Altitude =8cos(60°)
Altitude=4cm
Let the upper half of the altitude be y cm.
Then the radius of the circle is (y-4)cm
The upper radius meets the tangent at right angles.
From the smaller right triangle,
[tex] \sin(60 \degree) = \frac{4 - y}{y} [/tex]
[tex] y\sin(60 \degree) = 4 - y[/tex]
[tex]y\sin(60 \degree) + y= 4 [/tex]
[tex](\sin(60 \degree) + 1)y= 4 [/tex]
[tex]y= \frac{4}{\sin(60 \degree) + 1} [/tex]
[tex]y = 16 - 8 \sqrt{3} [/tex]
y=1.857
The diameter is 2y
[tex]d = 32 - 16 \sqrt{3} [/tex]
=2(1.875)
The length of a Diameter is 3.714
Answer:
Diameter of the circle is 16 cm.
Step-by-step explanation:
Given : The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm.
To find : The length of a diameter of the circle circumscribed about this triangle?
Solution :
We construct a circle in which an ABC isosceles triangle is formed.
Refer the attached figure below.
The measure of a vertex angle of an isosceles triangle is 120° .
The length of a leg is 8 cm, AC=8 cm
Vertex angle is divided by the line touching the center of the circle.
So, [tex]\angle A=60^\circ[/tex] and line AD=radius of the circle
Applying property of isosceles triangle,
Now, ∠DAC=∠ACD=∠CDA=60°
AC=DC=8 cm
The radius of the circle is 8 cm.
The diameter of the circle is twice the radius.
Therefore, The diameter of the circle is d=2(8)=16 cm.
I have no idea what to do.. someone please explain??
Answers
Answer:
d = 25 inches
Step-by-step explanation:
If the figures are similar, the dimensions have to be in proportion
diameter diameter
------------- = ------------
height height
10 ft d inches
------------- = ------------
4 ft 10 inches
Using cross products
10 * 10 = 4 *d
100 = 4 d
Divide by 4
100/4 =4d/4
25 = d
d = 25 inches
Check the picture below.
bearing in mind that the large cylinder is using feet units, and thee are 12 inches to 1 foot, thus 10 feet = 120 inches.
A survey of all teachers at a school found that the mean time planning for their classes is 54 minutes a day. Is the mean time a parameter or a statistic?
Answers
Answer:
Statistic
Step-by-step explanation:
You are asking more than one people/persons so it would be statistic.
If you increase your bicycle speed by 5.6 miles per hour, the speed will be 17.9 miles per hour. What is your bicycle speed now?
Answers
Answer:
12.3 mph
Step-by-step explanation:
17.9 - 5.6 = 12.3
Answer:
12.3 mph
Step-by-step explanation:
Let x be our speed now
We increase the speed by 5.6 mph
Our new speed is x+5.6
We are going 17.9 mph
x+5.6 = 17.9
Subtract 5.6 from each side
x+5.6 -5.6 = 17.9-5.6
x =12.3
What is the amplitude, period, and phase shift of f(x) = −4 sin(2x + π) − 5?
Amplitude = −4; period = 2π; phase shift: x = -pie/2
Amplitude = −4; period = π; phase shift: x = pie/2
Amplitude = 4; period = π; phase shift: x = -pie/2
Amplitude = 4; period = 2π; phase shift: x = pie/2
Answers
Answer:
Amplitude = 4; period = π; phase shift: x = -pie/2
Step-by-step explanation:
For a sine wave of the following type:
y = Asin(Bx + C) + D, we have that:
A represents the amplitude
C represents the phase shift
D represents the vertical shift
And the period is given by: [tex]\frac{2 \pi}{B}[/tex]
Therefore, considering: f(x) = −4 sin(2x + π) − 5, we know that sin(a + π) = -sin(a). Then:
f(x) = −4 sin(2x + π) − 5 = 4sin(2x)-5 = 4cos(2x - π/2) - 5
The amplitude equals 4
The period is T = π
The fase shift is: -π/2.
Therefore, the correct option is:
Amplitude = 4; period = π; phase shift: x = -pie/2
Is 27,36,45 A right trangle?
Answers
Answer:
We square the 2 smallest sides and sum them:
27^2 = 729 + 36^2 = 1,296
729 + 1,296 = 2,025
This equals the longest side squared 45^2 = 2,025
When this occurs the triangle is a right triangle.
Step-by-step explanation:
Given that he polynomial function below find f(-9)
Answers
Answer:
B
Step-by-step explanation:
To find the value [tex]F(-9)[/tex] of the polynomial function [tex]F(x)=-x^2-10x-2,[/tex] you have simply substitute [tex]x=-9[/tex] into the function expression (write -9 instead of x):
[tex]F(-9)=-(-9)^2-10\cdot(-9)-2\\ \\=-81+90-2\\ \\=7[/tex]
Final answer:
To find f(-9) in the given function, substitute -9 for x and evaluate by following the transformation rules.
Explanation:
We can rewrite a given function as y = f{-2(x+1)}. To find f(-9), we substitute -9 for x in the function.
This gives us f(-9) = f{-2(-9+1)}. Calculating further results in f(-9) = f{-2(-8)}.
Therefore, to find f(-9), we evaluate the function at x = -8, and the value depends on the specific function provided.
When Elyse moved last weekend, the circular glass top for an end table broke. To replace it, she bought a circular glass top with a diameter of 20 inches.
What is the approximate area of the circular glass top Elyse bought?
Answers
Answer:
A = 314 inches^2
Step-by-step explanation:
We know the diameter of the glass. We need to find the radius
d = 2r
20 = 2r
Divide each side by 2
20/2 = 2r/2
10 =r
To find the area of the glass
A = pi r^2
A = pi * 10^2
A = pi*100
A = 100 *(3.14)
= 314 in^2
Complete the Venn diagram.
Answers
in the junior side it is 22 the middle is 8 the girl side is 20 the outside is 16
Answer:
In sequence: 6, 8, 12 and 16
Step-by-step explanation:
Ok, the Venn diagram has 4 sections:
A - Juniors, but excluding girls (so boys only)
B - Juniors, who are also girls (so girls only)
C - Girls only, who aren't Juniors
D - Then outside the circles, for those who are not juniors and who are not girls (senior boys).
So, in A, you place the junior boys (6)
in B, you place the junior girls (8)
in C, you place the senior girls (12)
and in D, you place the senior boys (16)
the table shows the number of minutes of exercise for each person. compare and contrast the measures of variation for both weeks. please answer quickly and thank you!
Answers
To compare the measures of variation for both weeks, calculate the range and standard deviation. Week 1 has a larger range and standard deviation compared to Week 2.
Explanation:
To compare and contrast the measures of variation for both weeks, we need to calculate the range and standard deviation for each week. The range is the difference between the highest and lowest values, while the standard deviation measures the average amount by which each data point differs from the mean.
For Week 1, the range is 90 (90 - 30), and the standard deviation is 25.62. For Week 2, the range is 30 (60 - 30), and the standard deviation is 11.55.
Therefore, Week 1 has a larger range and standard deviation compared to Week 2.
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Which will hold more cake batter the rectangular pan or two round pans
Answers
Answer:
I don't know the size of the pans, but I'd probably say the rectangle ones.
Step-by-step explanation:
Y'know, you have to calculate volume and all that put based on the info given rectangular pans usually hold more...although there are two round pans...please add some numbers to clarify!