The relationship between the heights of the fence, the lengths, the distance below the ground level is an illustration of addition and subtraction.
The height of the fence is [tex]3\frac 38[/tex] in plan A and [tex]4\frac 34[/tex] in plan BThe fence in plan B is taller by [tex]2\frac{3}{4}[/tex] feet.The fence in plan B is recommended because: It is taller than the fence in plan A, and it goes below the ground level than plan AThey charge $136.88Plan A
[tex]Length = 4\frac 14[/tex]
[tex]Ground\ Level = \frac 78[/tex]
Plan B
[tex]Length = 6\frac 34[/tex]
[tex]Ground\ Level = 1\frac 12[/tex]
The height of the fence is calculated by subtracting the length below ground level from the length of the fence. So, we have:
[tex]Plan\ A = 4\frac 14 - \frac 78[/tex] [tex]Plan\ B = 6\frac 34 - 1\frac 12[/tex]
[tex]Plan\ A = \frac{17}{4} - \frac 78[/tex] [tex]Plan\ B = \frac{25}{4} - \frac 32[/tex]
Take LCM
[tex]Plan\ A = \frac{17\times 2 - 7}{8}[/tex] [tex]Plan\ B = \frac{25 - 3\times 2}{4}[/tex]
[tex]Plan\ A = \frac{34 - 7}{8}[/tex] [tex]Plan\ B = \frac{25-6}{4}[/tex]
[tex]Plan\ A = \frac{27}{8}[/tex] [tex]Plan\ B = \frac{19}{4}[/tex]
[tex]Plan\ A = 3\frac{3}{8}[/tex] [tex]Plan\ B = 4\frac{3}{4}[/tex]
Hence, the height of fence is [tex]3\frac 38[/tex] in plan A and [tex]4\frac 34[/tex] in plan B
The fence in plan B is taller because [tex]4\frac 34[/tex] is greater than [tex]3\frac 38[/tex]
The difference (d) in the heights is:
[tex]d = 4\frac 34 - 3\frac 38[/tex]
[tex]d = \frac{19}{4} - \frac{27}{8}[/tex]
Take LCM
[tex]d = \frac{19 \times 2 - 27}{4}[/tex]
[tex]d = \frac{38 - 27}{4}[/tex]
[tex]d = \frac{11}{4}[/tex]
[tex]d = 2\frac{3}{4}[/tex]
Fence in plan B is taller by [tex]2\frac{3}{4}[/tex] feet.
I will recommend the fence in plan B because:
It is taller than the fence in plan AIt goes below the ground level than plan AFor (5), we have:
[tex]Total = \$356.88[/tex]
[tex]Cash = \$220[/tex]
The remainder is the difference in the total amount and the amount they paid:
[tex]Charge = Total - Cash[/tex]
[tex]Charge = \$356.88 - \$220[/tex]
[tex]Charge = \$136.88[/tex]
Hence, they charge $136.88
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please help me with these ones ok
Answer:
first question: reflection on the y axis
second question: reflection on the x axis
Step-by-step explanation:
What is this expression in simplified form?
Answer:
B is answer.
Step-by-step explanation:
B is answer.
Find a2 and a3 for the geometric sequence 4, a2, a3, 108.
9514 1404 393
Answer:
a2 = 12
a3 = 36
Step-by-step explanation:
Terms of a geometric sequence have a common ratio. If we call that ratio r, then we have ...
a2 = 4r
a3 = (a2)r = 4r^2
108 = (a3)r = 4r^3
27 = r^3 . . . . . . . . . . . divide by 4
3 = r . . . . . . . . . . cube root
__
a2 = 4(3) = 12
a3 = 12(3) = 36
Last week Zurina worked the following days and times:
Day 1: 4 hours, 15 minutes
Day 2: 5 hours, 0 minutes
Day 3: 6 hours, 45 minutes
Find Zurina's total time worked in decimal hours. (4 points)
14.45
15.60
16.00
Answer:
46 hours and 5 minutes she worked
Answer is 15.60
we can say 4h and 15 min is 4.15
4.15 + 5.00 + 6.45 =
15.60
so the answer would be B
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The leaning tower of Pisa is approximately 179 ft in “height” and is approximately 16.5 ft out of plumb. Find the angle at which it deviates from the vertical.
The angle at which the leaning tower of Pisa deviates from the vertical is approximately 5.31 degrees.
To find the angle at which the leaning tower of Pisa deviates from the vertical, we can use the concept of tangent function.
First, we need to calculate the distance that the top of the tower is displaced from the vertical axis. This can be done using the Pythagorean theorem, which states that the displacement (d) is equal to the square root of the height of the tower (h) squared plus the amount the tower is out of plumb (p) squared:
d = √(h² + p²)
d = √(179² + 16.5²)
d = 180.14 ft
Next, we can use the tangent function to find the angle of deviation (θ):
tan(θ) = p/h
tan(θ) = 16.5/179
θ = tan⁻¹(16.5/179)
θ ≈ 5.31 degrees
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If an atom has 12
positively-charged
protons and 12
negatively charged
electrons, what is its
total charge?
Answer:
if both the electron and proton have the same number then the charge of an atom is neutral because each proton executes each neutron
How much simple interest would Lou Ann earn on a starting balance of $500 over 240 days at 3% simple interest assume ut us a 3645 day year? Justify your solution
Step-by-step explanation:
500 divided by 3 __
__ + 3645 = __
__ - 240 = __
Any mathematician to help me do this question.
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Answer:
70
Step-by-step explanation:
If we consider the terms to have decreasing powers of x, then the middle term is the one with x^4y^4 as its variables. The full value of that term is ...
(8C4)(2x)^4(3y)^4 = 70(6xy)^4
Substituting for x and y, this is ...
70(6(1/3)(1/2))^4 = 70(1^4) = 70
The middle term is 70 when (x, y) = (1/3, 1/2).
_____
The value of nCk is n!/(k!(n-k)!). Then 8C4 is 8!/(4!)^2 = (8·7·6·5)/(4·3·2·1) = 70.
1
What is the value of
60?
O
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I need help with this problem.
How do I do it?
Answer:
20
Step-by-step explanation:
For the area of a rectangle we use A = L* W
We know area or A = 420
and we know length or L = 21
Now we need to find the width or W
(420) = (21) * W
Divide both sides of the equation by 21 to isolate the variable.
That leaves us with:
W = 20
I will mark as brainliest:)
Answer:d
Step-by-step explanation:
- Three times the quantity two decreased by x is nine.
Step-by-step explanation:
3(2-x)=9
this is the answer to the statement
The expression three times the quantity two decreased by x is nine is - 1
A quantity two decreased by x can be expressed thus :
(2 - x)Multiplying the quantity by 3 :
3(2 - x)The expression can be written Mathematically as thus : 3(2 - x) = 9
The expression can be expanded further as :
3(2 - x) = 9
6 - 3x = 9
Collect like terms
-3x = 9 - 6
-3x = 3
x = (3 ÷ -3)
x = - 1
Therefore, the expression equates to - 1
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Is 0.03456 a rational number
Answer:
Yes. It is a rational number.
Find the unit rate. 7 square foot in - hour
i need more info. Is this the whole question?
what is the median of the number 10 12 13 15 16 19 25?
Answer:
15 is the middle number
Step-by-step explanation:
BECAUSE IF YOU COUNT FROM THE LEFT AND RIGHT AND WHICH NUMBER APPEARS IN THE MIDDLE IS YOUR MEDIAN
Answer:
15
Step-by-step explanation:
this asks for the median, and not the mean value.
please notice that these 2 values are often if not mostly different from each other.
the median just defines the middle of the value interval, so that half of the different values are left, and half are right of that median value.
here we have 7 values. do we find one, so that 3 other values are smaller, and 3 other values are bigger than that ?
that is 15.
10, 12, 13 are smaller.
16, 19 and 25 are bigger.
so, 15 is the median.
make d the subject of the formula h= d/3 + 2
Answer:
d= 3h-6
Step-by-step explanation:
h= d/3+2
h-2= d/3
d= 3(h-2)= 3h-6
Answer:
d = 3h - 6
Step-by-step explanation:
[tex]h = \frac{d}{3} + 2[/tex]
subtract 2 on all sides :
[tex](h) - 2 = (\frac{d}{3} + 2) - 2 \\ \\ h - 2 = \frac{d}{3} [/tex]
multiply 3 on all sides:
[tex](h - 2) \times 3= \frac{d}{3} \times 3 \\ \\ 3(h - 2) = d[/tex]
open bracket:
[tex]d = 3h - 6[/tex]
Can’t figure out number 32 plzzzz help
Answer:
Area = 80
Step-by-step explanation:
area = a^2 = 4^2 = 16 = square
area = wl = 12*8 = 96 = rectangle
rectangle - square
96 - 16 = 80
Evaluate the exponent expression for a = –2 and b = 3.
Answer:
The choose B) -9/8
Step-by-step explanation:
[tex] \frac{ - 2a ^{ - 3 } {b}^{2} }{a} \\ \frac{ - 2( - 2)^{ - 3} {3}^{2} }{ - 2} \\ \frac{ - 2(9)}{ - 2( - 8)} = - \frac{9}{8} [/tex]
I hope I helped you^_^
Which of the following does not represent a proportional relationship?
A. Zoe earns a base salary of $500 plus 3% commission
B. Dane drove 200 miles at a consistent speed for four hours
C. Water leaks from the faucet at a rate of 1/2 of a liter per hour
D. A recipe for biscuits calls for 3 cups of flour and 1 1/2 teaspoons of baking soda
Step-by-step explanation:
the correct aanswer is 3 is correct answermark me bbrainleast plz
Answer:
d is the answer
Step-by-step explanation:
mark me as brilliant
If it takes you 20 minutes to hike a distance of 1 mile, how fast are you walking in miles per hour
Answer:
1.60934 per hour
please mark me brainliest
Answer:
1.60934 per hour
plz mark my answer brainliest answer plz
kindly help answering the question.
Answer:
[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]
Or, their exact solutions:
[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle 2\sec^2 \theta = 4\tan \theta + 1[/tex]
For 0° ≤ θ ≤ 360°.
Recall that tan²(θ) + 1 = sec²(θ). Substitute:
[tex]\displaystyle 2\left(\tan^2 \theta + 1\right) = 4\tan \theta + 1[/tex]
Distribute:
[tex]\displaystyle 2\tan^2\theta + 2 = 4\tan\theta + 1[/tex]
Isolate:
[tex]\displaystyle 2\tan^2\theta - 4\tan\theta + 1 = 0[/tex]
This is in quadratic form. Thus, we can solve it like a quadratic. Let u = tan(θ). Hence:
[tex]\displaystyle 2u^2 - 4u + 1=0[/tex]
The equation is not factorable. Therefore, we can consider using the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}[/tex]
In this case, a = 2, b = -4, and c = 1. Substitute and evaluate:
[tex]\displaytstyle \begin{aligned} u &= \frac{-(-4)\pm\sqrt{(-4)^2 - 4(2)(1)}}{2(2)} \\ \\ &= \frac{4\pm\sqrt{8}}{4} \\ \\ &= \frac{4\pm2\sqrt{2}}{4} \\ \\ &= \frac{2\pm\sqrt{2}}{2}\end{aligned}[/tex]
Therefore:
[tex]\displaystyle u = \frac{2+\sqrt{2}}{2} \approx 1.7071\text{ or } u = \frac{2-\sqrt{2}}{2}\approx 0.2929[/tex]
Back-substitute:
[tex]\displaystyle \tan\theta = \frac{2+\sqrt{2}}{2} \text{ or } \tan \theta = \frac{2-\sqrt{2}}{2}[/tex]
Take the inverse tangent of both equations. Hence:
[tex]\displaystyle \theta = \arctan\frac{2+\sqrt{2}}{2} \approx 59.6388^\circ\text{ or } \theta = \arctan\frac{2-\sqrt{2}}{2}\approx 16.3249^\circ[/tex]
The same value of tangent occurs twice in every full rotation. Hence, by reference angles, the other two solutions are:
[tex]\displaystyle \theta = 180^\circ + \arctan\frac{2+\sqrt{2}}{2} \approx 239.6388^\circ \\ \\ \theta = 180^\circ + \arctan\frac{2-\sqrt{2}}{2} \approx 196.3249^\circ[/tex]
In conclusion, the four solutions are:
[tex]\displaystyle \theta = \left\{\arctan\frac{2-\sqrt{2}}{2} , \arctan\frac{2+\sqrt{2}}{2}, 180^\circ + \arctan\frac{2-\sqrt{2}}{2}, 180^\circ + \arctan\frac{2+\sqrt{2}}{2}\right\}[/tex]Or, approximately:
[tex]\displaytstyle \theta \approx \left\{16.3249^\circ, 59.6388^\circ, 196.3249^\circ, 239.6388^\circ\right\}[/tex]
Given P(A) = 0.6 and P(B) = 0.8, do the following. If A and B are independent events, compute P(A and B)
Answer:
0.48
Step-by-step explanation:
[tex]0.6*0.8 = 0.48[/tex]
simplify (y + 5 )-( y - 6)
Answer:
11
Step-by-step explanation:
(y+5)-(y-6)
y+5-y+6(opening the bracket)
5+6
11
Answer:
11
Step-by-step explanation:
(y+5) - (y-6) = y + 5 - y + 6 =
0y + 11 = 11
Remember, y - y = 1y - 1y = 0y or 0, and - (y-6) = -1 (y-6) = -y + 6
The ________ is the actual population of individuals, or clusters, from which a random sample will be drawn.
!! MATH EMERGENCY !! Hey Can someone please help me Ill give as many points as i can and make brainiest i just really need help
Answer:
B
Step-by-step explanation:
it simplifies to [tex]x^{4}[/tex]
Evaluate the expression below for x = 5. 5(x + 7)
Answer:
60
Step-by-step explanation:
5(x + 7)
when x is equal to 5, then
5(x + 7)5(5+7)5(12)5×12607. After 8 months, Joellen has lost 75 pounds. This is a 30% decrease in her starting weight. Find
her starting weight.
Answer:
Started 100% = x pounds
30% = 75 pounds
x= 75*100÷30= 250 pounds
Starting Weight = 250 pounds
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
30% = 75 pounds
100% = 250 pounds
The starting weight was 250 pounds.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
30% decrease = 75 pounds
Starting weight = 100%
Now,
30% = 75
Multiply 100/30 on both sides.
100/30 x 30% = 100/30 x 75 pounds
100% = 10/3x 75 pounds
100% = 10 x 25 pounds
100% = 250 pounds
Thus,
The starting weight was 250 pounds.
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Similarity and Congruence
Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent, and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
Each pair of figures is similar. Find the value of the missing side (x).
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Answer:
3 in
Step-by-step explanation:
Ratios of corresponding sides are equal, so we have the proportion ...
x/(5 in) = (6 in)/(10 in)
x = (5 in)(6/10) = 3 in
The missing side (x) is 3 in.
What is the equation of a line parallel to y=1/3x-4 that passes through (9,8)?
Step-by-step explanation:
Given line y=1/3x-4
slope of given line m=1/3
Slope of required line :
m=1/3
As lines are parallel then slope of lines are equal.
Using point slope form:
y-y1=m(x-x1)
p(x1,y1)=(9,8)
y-8=1/3(x-9)
3y-24=x-9
x-3y-9+24=0
x-3y+15=0
Note:if you need to ask any question please let me know.
IF
(3x + y = 10
\x-4y=-1
then
n y =
Answer:
n | 0 | 0 1
| y 2 | 2 y 3 | 3 años
Step-by-step explanation: