Solution
Given that
Area f small square = 40 inches squared.
[tex]\begin{gathered} a=40 \\ \\ \text{ since a}=l^2 \\ \\ \Rightarrow40=l^2 \\ \\ \Rightarrow l=\sqrt{40} \end{gathered}[/tex]Let the side of the large square be L
Since the large square has sides that are 8 times longer than the small square
=> L = 8l
[tex]\begin{gathered} \Rightarrow L=8l \\ \\ \Rightarrow L=8(\sqrt{40}) \end{gathered}[/tex]Hence, the area of Large square is;
[tex]A=L^2=(8\sqrt{40})^2=64\times40=256[/tex]Hence, the area of the large square is: 256 inches squared.
Aaron has a smart phone data plan that costs $40 per month that
includes 6 GB of data, but will charge an extra $25 per GB over the
included amount. How much would Aaron have to pay in a month
where he used 3 GB over the limit? How much would Aaron have to
pay in a month where he used went over by x GB?
Total cost when over by 3 GB:
Total cost when over by x GB:
Pls give me correct answer
I need it or else I fail
Aaron has to pay $ 115 when the usage gets over by 3 GBs and
$ (40 + 25x) when the usage gets over by x GBs.
How can one calculate the cost for a multiple of the same entity?
To calculate the cost of a multiple entities when the cost of a single one is given, we linearly multiply a fixed proportion to it to calculate the same.
Given, monthly fixed cost of the smart phone data plan = $ 40
Also, amount charged by the firm for each extra GB used = $ 25
Now, amount charged for three extra GBs = 25*3 = 75
Thus, net total that Aaron has to pay for 9 GBs = 40 + 75 = $ 115
Following similar arguments, amount charged for extra 'x' GBs = 25x
Thus, net total that Aaron has to pay for x GBs = 40 + 25x = $ (40 + 25x)
Therefore, Aaron has to pay $ 115 when the usage gets over by 3 GBs and $ (40 + 25x) when the usage gets over by x GBs.
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I would really appreciate your help
Answer:
The answer is 35
Step-by-step explanation:
Pls mark this answer as brainliest
I really need help on this!
Answer:
chad's other friend picked up 1 3/8 pounds of berries
Step-by-step explanation:
chad = 2 1/2 = 2 4/8
friend 1 = 1 3/8
2 4/8 + 1 3/8 = 3 7/8
5 1/4 = 5 2/8
5 2/8 - 3 7/8 = 1 3/8
Please help simple math 50 points
Answer:
2 pizzas
Step-by-step explanation:
5 7/8 - 4 1/16=
5 14/16 - 4 1/16 ==> make the denominators equal to each other so they can be easily subtracted in the next step
5 + 14/16 - (4 + 1/16)=
5 + 14/16 - 4 - 1/16 =
5 - 4 + 14/16 - 1/16 =
1 + 13/16 = 1 13/16 which is approximately 2 pizzas
when a grizzly bear hibernates, its heart rate drops to 101010 beats per minute, which is 20\ , percent of its normal value. what is a grizzly bear's normal heart rate when not hibernating? beats per minute
A grizzly bear's normal heart rate when not hibernating is 50 beats per minute.
What is a heart rate?
The number of heartbeats that occur in a specific amount of time, usually one minute. The wrist, side of the neck, back of the knees, top of the foot, groin, and other areas of the body where an artery is close to the skin can all detect the heartbeat.
Here,
We let his normal heart rate = h
and given in the question,
20% of h = 10
20/100 * h = 10
h = 10*5
= 50 beats/min
Hence, a grizzly bear's normal heart rate when not hibernating is 50 beats per minute.
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a water tank is to contain 2,000 liters of water it is constructed to be 4 meters long and 1.5 meters wide. find the height of the tank.
Remember that
1 m3=1,000 lt
2 m3=2,000 lt
The volume of the tank is equal to
V=L*W*H
we have
V=2 m3
L=4 m
W=1.5 m
H=?
substitute given values
2=4*1.5*H
solve for H
2=6H
H=2/6
H=1/3 mCould someone please help me this is due at 3 pm and it's allready 2:43 and i only need these questions and i am done please help me. if you answer all you get 20 points! PLEASE HELP PLEASE HELP ANYONE PLEASE PLEASE
a) (2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex]) in standard form
The number in standard form is 345
explanation:
The given two multiplication of the numbers is :
(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])
First we multiply the non exponential terms as shown below
2.3 × 1.5 = 3.45
Now we multiply the exponential terms as shown below
[tex]$10^4[/tex] × [tex]$10^{-2}[/tex] = 100
Now multiplying the exponential and non exponential term we get the number in standard form as shown below
(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex]) in standard form 345
(3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form 0.0000002
(8 × 10^-3) × (2 × [tex]10^-4[/tex] in standard form 1.6 × [tex]10^-6[/tex]
(6 × 10²)/(3 × 10-5) in standard form 20,00,0000
5.1 × [tex]$10^-1[/tex] in ordinary number is 0.51
(1.7 × [tex]10^4[/tex]) × (8.5x ×[tex]0^-2[/tex]) in standard form 1.445 × 10³.
3.45 x 100 = 345
Therefore, the number in the standard form is 345
b) (3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form
The number in standard form is 0.0000002
explanation:
By dividing 3.6 by 1.8 we get “2”, hence the above equation becomes,
(2 × [tex]10^-5[/tex]) /[tex]10^2[/tex]
We know that
[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]
Therefore the above equation becomes,
2 × [tex]10^-7[/tex]
since the exponent of 10 is negative , therefore 7 zeros are written on the left hand side of the number = 0.0000002
Therefore, the number in the standard form is 0.0000002
c) (8 × [tex]10^-3[/tex]) × (2 × [tex]10^-4[/tex]) in standard form
The number in standard form is 1.6 × [tex]10^-6[/tex]
explanation:
Given the product of scientific notations:
(8 × [tex]10^-3[/tex]) × (2 × [tex]10^-4[/tex])
This can be expressed as:
(8 × 2) × ([tex]10^-3[/tex] × [tex]10^-4[/tex])
= 16 × [tex]10^-3[/tex]-4
= 16 × [tex]10^-7[/tex]
= 1.6 × [tex]10^1[/tex] × [tex]10^-7[/tex]
= 1.6 × [tex]10^-6[/tex]
Therefore, the number in the standard form is 1.6 × [tex]10^-6[/tex]
d) (6 × 10²)/(3 × 10-5) in standard form
The number in standard form is 20,00,0000
e) 5.1 × 10^-1 as an ordinary number
The ordinary number is 0.51
usual form of 5.1 × [tex]10^1[/tex] is
5.1 × 1/ [tex]10^1[/tex]
= 5.1/10
= 0.51
Therefore , ordinary number is 0.51
f) (1.7 × [tex]10^4[/tex]) × (8.5 × [tex]10^-2[/tex]) in standard form.
The number in standard form is 1.445 × 10³.
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If f(x) is an exponential functionwhere f(-2) = 1 and f(7) = = 63,then find the value of f(1) , to thenearest hundredth.
An exponential function has the form
[tex]y=ab^x[/tex]Therefore, to find an exponential function that satisfies our condition, we need to find a and b.
From f(-2) = 1, we have
[tex]1=ab^{-2}\: ^{}\: \: \: \: \; ^{}\: \: \: \: \; (1)[/tex]and from f(7) = 63, we have
[tex]63=ab^7\: \: \: \: \; ^{}\: \: \: \: \; (2)[/tex]Solving for a in equation (1) gives
[tex]a=b^2[/tex]substituting this value of a into equation (2) gives
[tex]63=b^2\cdot b^7[/tex][tex]63=b^8[/tex][tex]\begin{gathered} \therefore b=\sqrt[8]{63} \\ b=1.6785 \end{gathered}[/tex]With the value of b in hand, we now find the value of a:
[tex]\begin{gathered} a=b^2 \\ \therefore a=2.8173 \end{gathered}[/tex]Hence, the exponential function is
[tex]f(x)=(2.8173)(1.6785)^x[/tex]Evaluating the above function at x = 1 gives
[tex]\begin{gathered} f(1)=(2.8173)(1.6785)^1 \\ \boxed{\therefore f(1)=4.73.} \end{gathered}[/tex]which is our answer!
1/3 divided by 2 (1/2)^3
please help me
Answer:
1/24
Step-by-step explanation:
.........................
Answer:
I'll assume that "2 (1/2)^3" means 2*(1/2)^3.
Step-by-step explanation:
(1/3)/(2*(1/2)^3)
(1/3)/(1)^3
= (1/3)
===========================
If "2(1/2)^3" means (2+1/2)^2:
((5/2)^2 = (25/4)
--
(1/3)/(25/4)
(1/3)*(4/25) = 4/75 or 0.05333
What’s 1+1 I need to know asap
Answer:
2
Step-by-step explanation:
convert 1 + the other one is 2
Answer:
2
Step-by-step explanation:
You add both numbers that have been given which are 1+1
PLEASE HELP ASAPPP!!!!
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.
What is the standard form of the equation of f(x)?
f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7
Answer:
f(x)= -x^2-6x+7
Step-by-step explanation:
Since the graph opens downward the function for the parabola is going to be negative. This leaves us with two answers.
Now use the remaining possible equations and solve for the vertex.
Using x= -b/2a to solve for the x value of the vertex plug in the values to solve.
a= -1 b= -6 c=7 so, since -6 is already negative plugging it in makes it positive -(-6)/2(-1) = 6/-2 = -3. So x equals negative 3.
Then plug in -3 into the equation to get the y-value.
- (-3)^2 - 6(-3) + 7 = -9 + 18 + 7 = 16 so this confirms the vertex for this equation is (-3,16) so the answer is -x^2-6x+7.
Hope this helped! :)
Amy found that she could use the function P(t)=3t^2+5t+8 to model the population of a collection of fruit flies over time, where t is the time in days and P(t) is the number of flies. According to her model, how many flies will there be after 16 days?
A: 8
B: 768
C: 856
D: 2204
The total number of files after 16 days using the function P(t) = 3t² + 5t + 8 is 856.
A relationship between a group of inputs having different outputs is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output.
The function P(t) represents the population of a collection of fruit flies at a particular time in days.
P(t) is the number of flies and t is the time in days.
Now, consider the function:
P(t) = 3t² + 5t + 8
Therefore, the number of flies after 16 days will be:
When t = 16,
P(t) = 3t² + 5t + 8
P(16) = 3(16)² + 5(16) + 8
P(16) = 3 × 16 × 16 + 5 × 16 + 8
P(16) = 768 + 80 + 8
P(16) = 856
Hence, the number of flies after 16 days will be 856 flies using the function P(t).
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If n in an odd integer that is less than -3.25, what is the greatest possible value of n?
The greatest possible value of n is -5
How to determine the possible value of n?From the question, the given parameters are:
n = Odd integerN is less than -3.25The second highlight above can be represented as
n < -3.25
Since n is an integer, then the possible values of n are
n = -4, -5, -6, -7, -8....
Remove the even integers from the above list of numbers because n is an odd integer
So, we have
n = -5, -7, -9....
The greatest value above is n
This means that n can have the highest value of -5
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What is the value of this expression.
here's your answer hope it helps
(01.06 MC)
Ray IL bisects angle HIJ. If mzHIL = (6x - 7)° and mzJIL = (5x + 4)°, what is mzJIL?
118°
59°
44°
11°
Option C, 59° is correct answer, The angle JIL is equal to 59 degree.
What is angle?
Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.
Given information in the question,
∠HIL = (6x-7)°
∠JIL = (5x+4)°
The ray IL bisects the ∠HIJ
Since, IL bisects angle HIJ then, angle HIL = angle JIL
So,
6x - 7 = 5x + 4
x = 11
Putting the value of x in given value of JIL to get the angle JIL
∠JIL = (6x-7)°
∠JIL = (6(11)-7)°
∠JIL = 59°
Therefore angle JIL is equal to 59 degrees.
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(MULTIPLE CHOICE) Write an expression that would represent the perimeter of a rectangle with a width of 10n and a length of 4.
A) 10n + 4 + 10n + 4
B) 10n + 4
C) 4(20n) (this is multiplication)
D) 10 + 4 + 20n + 4
5. Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the x-axis of the graph off(x) = -(x+3)^2 - 2. Write a rule for g.
Answer:
[tex]g(x)=-f(x-2)+2[/tex]Explanation:
Given the function f(x)
A translation of 2 units up = f(x)+2
Next, a translation of 2 units right = f(x-2)+2
When we reflect the result above in the x-axis, we have:
[tex]g(x)=-f(x-2)+2[/tex]A rule for g is therefore:
[tex]g(x)=-f(x-2)+2[/tex]Given the linear function in slope-intercept, what is the slope
and y-intercept of this line?
f(x) = x +9
Select TWO answers.
Answer:
Slope is 1 and y-intercept is 9
Step-by-step explanation:
y=mx+b
The slope is the coefficient of x in this case it would be 1
The y-intercept is whatever b is and it is +9 so it is 9
Kuta Software In Systems of Two Solve each system by graphing. 2) y=x+2 1) y=-3x +41 y= 3x - 2
ok
Equations : 4x + y = 2 x - y = 3
Equation 1 4x + y = 2 x - y = 3
x y x y
-2 10 -2 -5
-1 6 -1 -4
0 2 0 -3
1 -2 1 -2
2 -6 2 -1
The point where both lines cross is (1, -2) so it is the solution.
Graph line with slope 1/2 passing through the point (-1,3)
Answer:
Step-by-step explanation:
First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)
Dwayne is making a poster about friendship in his art class. He divides his poster into 12 equal parts. Dwayne writes the names of his friends all over each part. Dwayne uses 7 parts for his neighborhood friends and 5 parts for his friends from school. What fraction of the poster does Dwayne use for his friends from school?
The fraction of the poster does Dwayne use for his friends from school is 5/12.
What is the fraction of the poster that Dwayne uses for his friends from school?A fraction is a non-integer that has a numerator and a denominator. The numerator is the number that is above the line and the denominator is the number below the line. An example of a fraction is 5/12.
In this question, the numerator is the number of parts he gives his friends from school. The denominator is the total number of parts he divides the poster.
Fraction = parts he gave his friend from school / total number of parts
5 / 12.
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In the figure below fg = 18 and gh= 19 find fh
Answer:
18*19 BECAUSE 19 is a prime number and g has to be 1 since if g was anything else like 2 it wouldn't be the same for gh
32+40+…+120=? Someone help PLEASE
Answer:
912
Step-by-step explanation:
the assumption is that this is an arithmetic progression
the nth term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
use this to find which term 120 is in the sequence
with a₁ = 32 and d = a₂ - a₁ = 40 - 32 = 8 , then
32 + 8(n - 1) = 120 ( subtract 32 from both sides )
8(n - 1) = 88 ( divide both sides by 8 )
n - 1 = 11 ( add 1 to both sides )
n = 12
given the first and last terms in the sequence then sum is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last)
S₁₂ = [tex]\frac{12}{2}[/tex] (32 + 120) = 6 × 152 = 912
Donna bought 5 bags of dog treats for $12.50. What is the cost per bag of dog treats?
I really need help on this please guys
Answer:
2.5
Step-by-step explanation:
$12.50 ÷ 5 bags = $2.5 per bag
Answer:
2.50
Expination:
devide 12.50 by the total amount of dog food purchased (5 bags)
12.50/5 = 2.50
the price per bag is $2.50
The radius of a circle is 18 miles. What is the area of a sector bounded by a 72° arc?Give the exact answer in simplest form. ____ square miles. (pi, fraction,)
Area = (π*r^2*α)/360°
α =72°
r = 9 mi
Then
A = (π * 81 * 72°)/360° = 81/5π square meters
What’s the answer plss I really need help
Answer:
The answer is d) 22.4
Step-by-step explanation:
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The required equation of line would be 2y = 5x - 8 which is shown in the given graph.
What is the slope of the line?The slope of a line is defined as the angle of the line.
According to the given figure,
We clearly see that the coordinates of the y-intercept would be (0, -4).
The value of the x-coordinate is 2 when y-coordinate is 1.
Here the line passes through the points (0, -4) and (2, 1).
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]
x₁ = 0, y₁ = -4
x₂ = 2, y₂ = 1
⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
⇒ y - 1 = (1 - (-4))/(2 - 0 )[x -2]
⇒ y - 1 = 5/2[x -2]
⇒ 2y - 2 = 5[x -2]
⇒ 2y = 5x - 10 + 2
⇒ 2y = 5x - 8
Therefore, the required equation of line would be 2y = 5x - 8 which is shown in the given graph.
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Suppose that R(x) is a polynomial of degree 13 whose coefficients are real numbers. also, suppose that R(x) has the following zeros. answer the following.edit: if possible please double check the answers just to be safe.
(a) Complex zeros of a polynomial come in pairs.
If a + bi is a zero of a polynomial then its conjugate a - bi is also a zero of the polynomial.
The given complex zeros of R(x) are 1 + 3i and -2i.
1 - 3i is the conjugate of 1 + 3i.
Hence, another zero of R(x) is 1 - 3i
b)
Since the polynomial R(x) is of order 13 then R(x) must have 13 zeros.
The given complex zeros of R(x) are 1 + 3i and -2i. We also know that the conjugates of 1 + 3i and -2i are zeros of R(x). Hence, R(x) has at least 4 complex roots
Hence, the maximum number of real zeros of R(x) is (13 -4).
The maximum number of real zeros of R(x) is 9
c) Let the maximum number of nonreal zeros (complex roots) be n
Complex roots come in pairs. Therefore, n must be even.
Hence, n ≤ 13 - 1 = 12
n ≤ 10
We have been given a real zero of R(x), 3 ( With the multiplicity of 4).
12 - 4 = 8
Therefore,
n ≤ 8.
Hence the maximum number of nonreal zeros of R(x) is 8
The corner grocery store sells bananas for $2.91 per pound. Select the store that sells bananas at a lower unit price. Mark all that apply.Store A: $8.16 for 4 poundsStore B: $6.51 for 3 poundsStore C: $2.66 for 2 poundsStore D: $11.40 for 4 pounds
Let's find the unit price of each store
Store A : $8.16 /4 = $2.04 per pound
store B: $6.51 / 3 = $2.17 per pound
store c: $2.66 / 2 = $1.33 per pound
store D : $11.40 / 4 = $ 2.85 per pound
Therefore, store A, store B, store C and store D sells at a lower unit price than Corner grocery store.
1. Alex and chris share sweets
In ratio Alex : Chris= 7:3
Work out the number of
Sweets chris recieves.
Using ratios, we can conclude that Chris gets 12 sweets.
What are ratios?In mathematics, a ratio shows how many times one number is represented by another. If there are eight oranges and six lemons in a bowl of fruit, the proportion of oranges to lemons would be eight to six. 8:14 for oranges and 6:8 for lemons, respectively, are the ratios of oranges to the total amount of fruit.So, a number of sweets Chris receive:
Alex : Chris = 7:3Let, Chris sweets be 'x' and Alex sweets be 'x + 20'Now, 7:3 = x+20:x, solve as follows:
7:3 = x+20:x7/3 = x+20/x7x = 2x + 607x - 2x = 605x = 60x = 60/5x = 12
Therefore, using ratios, we can conclude that Chris gets 12 sweets.
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The correct question is given below:
Alex and Chris share sweets in the ratio Alex: Chris = 7 : 3. Alex receives 20 more sweets than Chris. Work out the number of sweets Chris receives.