Step-by-step explanation:
length = breadth + 5
the perimeter is a rectangle is
2×length + 2×breadth
in our case
2×length + 2×breadth = 74
so, we use the first equation in the second equation :
2×(breadth + 5) + 2×breadth = 74
2× breadth + 10 + 2× breadth = 74
4×breadth = 64
breadth = 16 m
length = breadth + 5 = 16 + 5 = 21 m
A rectangular room is 1.2times as long as it is wide, and its perimeter is
30 meters. Find the dimension of the room.
The length is :
meters and the width is
___meters.
The length is 6.8 meters and the width is 8.2 meters.
How to determine the dimension of the room?Represent the length and the width with x and y
So, we have:
y = 1.2x
P = 2(x + y)
The perimeter is 30.
So, we have:
2(x + y) = 30
Divide by 2
x + y = 15
Substitute y = 1.2x
x + 1.2x = 15
This gives
2.2x = 15
Divide by 2.2
x = 6.8
Substitute x = 6.8 in y = 1.2x
y = 1.2 * 6.8
Evaluate
y = 8.2
Hence, the length is 6.8 meters and the width is 8.2 meters.
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Elian's credit card had a balance of $132.20 on April 1. On April 5, he charged $74.50. On April 18, he made a payment of $52. On April 22, hecharged $18.75 and did not use the credit card the rest of the month. What was his average daily balance? $166.76 $173.45 $206.70 $179.86
Answer:
I iitiriririrrifjjrjr idiocy jdkthink 179.86
Which statements about the system are true? Select two options.
y=-x-4
3y-x = -7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The slope for both the line is m= 1/3 and they are parallel lines , Option B and C are correct two options
The first equation is
y = (1/3)x-4 and not y = -x-4
(if the equation is not corrected then it will not have two true statements)
What is a System of Equation ?A system of equation is a set of equation which have a common solution
The given system of equation is
y = (1/3)x-4
3y -x = -7
3y = x-7
As it can seen from the standard equation of a line that
y =mx+c
so slope for both the line is m= 1/3
Therefore they are parallel lines
Thus , Option B and C are correct two options
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If f(1) = 2 and f(n) = f(n − 1)² + 4 then find the value of ƒ (3).
Answer:
f(3) = 68
Step-by-step explanation:
→ f(1) = 2 ⇒ f(2) = f²(2 − 1) + 4
= f²(1) + 4
= 2² + 4
= 8
………………………………………………
→ f(2) = 8 ⇒ f(3) = f²(3 − 1) + 4
= f²(2) + 4
= 8² + 4
= 64 + 4
= 68
Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 3 hours the trains are 315 miles apart. Find the speed of each train
Answer:
Step-by-step explanation:
when finding the margin of error of the mean of a normally distributed population from a sample, what is the critical probability, assuming a confindence level of 58%
The critical probability, assuming a confindence level of 58% is 0.79.
How to calculate probability?From the information given, the confidence level is 58%. The alpha will be:
= 1 - (58/100)
= 1 - 0.58
= 0.42
The critical probability will be:
= 1 - (0.42/2)
= 1 - 0.21
= 0.79
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Simplify (27-17)^2-80
Answer:
-60
Step-by-step explanation:
On a coordinate plane, 2 cube root functions are shown. Function f (x) goes through (negative 3, negative 1.5), has an inflection point at (0, 0), and goes through (3, 1.5). Function g (x) is 2 units to the left of f (x) and has an inflection point at (negative 2, 0).
The graph of f(x) = RootIndex 3 StartRoot x EndRoot is shown with g(x). Which equation represents the graph of g(x)?
g(x) = RootIndex 3 StartRoot x minus 2 EndRoot
g(x) = RootIndex 3 StartRoot x + 2 EndRoot
g(x) = RootIndex 3 StartRoot x EndRoot + 1
g(x) = RootIndex 3 StartRoot x EndRoot–1
Using translation concepts, it is found that the equation that represents the graph of g(x) is:
[tex]g(x) = \sqrt[3]{x + 2}[/tex].
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have that g(x) is a shift left of 2 units of f(x), hence:
[tex]f(x) = \sqrt[3]{x}[/tex][tex]g(x) = f(x + 2) = \sqrt[3]{x + 2}[/tex]More can be learned about translation concepts at https://brainly.com/question/4521517
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Answer:
The answer is B. On EDGE.2022
Step-by-step explanation:
Just did it
find the indicated side of the right triangle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 3\sqrt3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \tan(60) = \cfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{3} = \dfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: x = 3 \sqrt{3} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Need help ASAP, will mark brainliest if you can check my answer:
According to the compound interest model, we find the following results: I) x ≈ 11.5 yr, C' = $ 101317.36, II) r ≈ 7.4 %, x ≈ 9.8 yr, III) C = $ 7626.38, x ≈ 8.6 yr, IV) r ≈ 6.5 %, C = $ 12801.61
How to determined all the variables associated with compound interest
Compound interest describes the capital gain in term of deposited capital and the consideration that such capital is increased continuously in time. The compound interest model is shown below:
C' = C · (1 + r/100)ˣ (1)
Where:
C - Initial capitalC' - Current capital r - Interest rate, in percentage.t - Time, in yearsThe doubling time (x) is the period needed for a capital to be doubled. It is described by the following expression based on (1):
x = (㏒ 2)/[㏒ (1 + r/100)] (2)
Now we proceed to calculate each missing variable:
Case I - Doubling time
x = (㏒ 2)/[㏒ (1 + 6.2/100)]
x ≈ 11.5
Case I - Current capital
C' = 75000 · (1 + 6.2/100)⁵
C' = 101317.36
Case II - Interest rate
[tex]r = 100\cdot \left(\sqrt [5] {\frac{7130.90}{5000} }-1\right)[/tex]
r ≈ 7.4
Case II - Doubling time
x = (㏒ 2)/[㏒ (1 + 7.3/100)]
x ≈ 9.8
Case III - Initial capital
C = 11414.71/(1 + 8.4/100)⁵
C = 7626.38
Case III - Doubling time
x = (㏒ 2)/[㏒ (1 + 8.4/100)]
x ≈ 8.6
Case IV - Interest rate
[tex]r = 100\cdot \left(\sqrt [11] {2 }-1\right)[/tex]
r ≈ 6.5
Case IV - Initial capital
C = 17539.32/(1 + 6.5/100)⁵
C = 12801.61
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Which statements about the system are true? Select two options.
y=-x-4
3y - x = -7
O The system has one solution.
O The system consists of parallel lines.
O Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
The system of equation has one solution
How to determine the true statements?The equations are given as:
y = -x - 4
3y -x = -7
Rewrite the first equation as:
y + x = -4
Add y + x = -4 to the second equation to eliminate x
4y = -11
Divide by 4
y = -11/4
Substitute y = -11/4 in y + x = -4
-11/4 + x = -4
Make x the subject
x = -4 + 11/4
Evaluate
x = -5/4
The above means that the system of equation has one solution
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Option A and B. The system has one solution and the system consists of parallel lines.
Slope of the linesThe slope of the lines is calculated as follows;
y = -x - 4
slope = - 1
3y - x = -7
3y = x - 7
y = x/3 - 7/3
slope = 1/3
Solution of the equationsy = -x - 4 ----(1)
3y - x = -7 ----(2)
solve (1) and (2)
3(-x - 4) - x = -7
-3x -12 - x = -7
-4x = 5
x = -5/4
y = -5/4 - 4
y = -5.25
Thus, the system has one solution and the system consists of parallel lines.
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Which of the following could be the first step in solving the equation below 4+2log_(3)x=17
Answer:
subract 4 from both sides
Step-by-step explanation:
5. There are 2 boys and 3 girls in the class. The
ratio of boys to girls in the class is equal to all
of the following except
Answer:
9:12
Step-by-step explanation:
since the others are multiples of 2:3
but 9:12 is not a multiple
Write 1 3/5 as an improper fraction?
Find the solution to the following system by substitution.
5x + y = 20
y = 5x
A. (2,10)
B. (4,0)
C. (0,20)
D. (4,20)
Answer:
A. (2,10)
Step-by-step explanation:
5x + y = 20
y = 5x
The second equation is already solved for y, so substitute 5x for y in the first equation to find x.
5x + 5x = 20
10x = 20
x = 2
Now substitute 2 for x in the second original equation to find y.
y = 5(2)
y = 10
Answer: (2, 10) which is A.
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P ( X > 2 ) , n = 5 , p = 0.7
The value of the probability P(x > 2) is 0.8369
How to evaluate the probability?The given parameters are:
n = 5
p =0.7
The probability is calculated as:
[tex]P(x) = ^nC_x *p^x * (1 - p)^x[/tex]
Using the complement rule, we have:
P(x > 2) = 1 - P(0) - P(1) - P(2)
Where:
[tex]P(0) = ^5C_0 *0.7^0 * (1 - 0.7)^5[/tex]
P(0) = 1 *1 * (1 - 0.7)^5 = 0.00243
[tex]P(1) = ^5C_1 *0.7^1 * (1 - 0.7)^4[/tex]
P(1) = 5 *0.7^1 * (1 - 0.7)^4 = 0.02835
[tex]P(2) = ^5C_2 *0.7^2 * (1 - 0.7)^3[/tex]
P(2) = 10 *0.7^2 * (1 - 0.7)^3 = 0.1323
Recall that:
P(x > 2) = 1 - P(0) - P(1) - P(2)
So, we have:
P(x > 2) = 1 - 0.00243 - 0.02835 - 0.1323
Evaluate
P(x > 2) = 0.83692
Approximate
P(x > 2) = 0.8369
Hence, the value of the probability P(x > 2) is 0.8369
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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 2.0. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003?
Answer:
1,887,436,800
Step-by-step explanation:
f(t) = a·b^t
f (t) = number of cases at year t
a = starting value = 1800 in 1983
b = growth factor = 2
t = years since 1983 = 2003 - 1983 = 20
f(t) = 1800·(2)^20 =
1,887,436,800
wyzant
philip p
The price of 11 pizzas and 5 hamburgers is 40$. The price of 1
hamburger is 2.50$. What is the price of a hamburger?
Step-by-step explanation:
you mean, what is the price of a pizza, right ? and I guess it is pizza slices ...
1 hamburger = $2.50
5 hamburgers = 5×1 hamburger = 5×2.5 = $12.50
that leaves for the 11 pizzas (slices)
40 - 12.5 = $27.50
so, 1 pizza (slice) is
27.5 / 11 = $2.50
Answer:
One hamburger costs $2.50
One pizza also costs $2.50
Step-by-step explanation:
Let's say Nigel is the one purchasing lots of food for no reason.
Nigel bought 11 pizzas and 5 hamburgers for $40 (DAMMMM WHAT COUPON IS THAT??)
We can write this algebraically:
11p + 5b = 40
We know that the price of 1 Hamburger is $2.50.
Now we can plug that into out equation and find the price of one pizza:
11p + 5(2.50) = 40
11p + 12.5 = 40
11p = 27.5
p = 2.5
Now, we have the price of one pizza, $2.50
What is the solution to t - 3 < 12
Answer:
[tex]\boxed {t < 15}[/tex]
Step-by-step explanation:
Given :
⇒ t - 3 < 12
Add 3 to each side :
⇒ t - 3 + 3 < 12 + 3
⇒ t < 15
Answer: t < 15
Step-by-step explanation:
rearrange the terms t - 3 < 12
calculate the sum or difference t < 12 + 3
answer t < 15
Use the graph of the parabola to fill in the table
(a) The parabola opens downward.
(b) The axis of symmetry is at x = -2.
(c) The vertex is at (-2,0).
(d) The x-intercepts is (-2,0), and the y-intercept is at (0,-1).
Are the two triangles congruent?
Answer:
yes.......................
Step-by-step explanation:
Which linear equation has a slope of 3 and a y-intercept of -2?
y = 3x + 2
y = 3x - 2
y = -2x + 3
y=-2x-3
Answer:
y = 3x - 2
Step-by-step explanation:
The number beside the x is the slope. The number at the end of the equation is the y-intercept.
All the answers are in this form:
y = mx + b
m is the slope.
b is the y-intercept.
With a 3 filled in for slope and -2 filled in for the y-intercept, you get:
y = 3x + -2
is the same as,
y = 3x - 2
Solve the equation.
-x+8+3x = x-6
O x=-18
O x=-14
O x = 2
O x = 4
Answer:
x = -14
Step-by-step explanation:
- x + 8 + 3x = x - 6
- x + 8 + 3x - x + 6 = 0
x + 14 = 0
x = -14
8.6 - 4 x 2 + 3/10 please i need this answer
Answer:
0.9
Step-by-step explanation:
What is one possible value of 2x
Answer:
really good
Step-by-step explanation:
thanks for your help you with that do not have a copy of the receipt for your time to help you with theASAP NOW! PLSS! I WILL MARK 5 STARS! PLSSS! thank you!! At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix. What was the temperature in each city? Explain your reasoning.
Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.
What are opposite values?Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.
In general, the temperature equation for Portland, Maine is stated mathematically as
PoT=-PhT
As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,
PoT=-PhT
PhT =+PoT
Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.
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What type of polynomial is P(x)=2+x?
Answer: linear polynomial
Step-by-step explanation:
What is the slope of the line through (1,-2) and (-3,-2)?
-1/2
Step-by-step explanation:
m = y2-y1/x2-x1
-3+2/3-1
m=-1/2
Hii!
_________________________________________________________________
Answer: Slope = 2 - Choice [C] ✅
Step-by-step explanation:
Do you need to know the slope of the line through (1,-2) and (-3,-2)? No problem! Luckily, there's a formula to find this!
The slope formulaThe slope formula "[tex]\sf \cfrac{y2-y1}{x2-x1}[/tex]", is the formula we'll use to find the slope.
Let's stick in the values we know
[tex]\sf m= \cfrac{-2-2}{-3-(-1)}[/tex]
Simplify
[tex]\sf m=\cfrac{-4}{-3+1}[/tex]
Simplify
[tex]\sf m=\cfrac{-4}{-2}[/tex]
[tex]\sf m= \cfrac{4}{2}[/tex]
[tex]\sf m=2[/tex] ✅
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Hope that this helped! Best wishes.
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A shopkeeper buys 72 articles for $82.80. How much will he have to pay if he buys 150 such articles.
Answer: He have to pay $172.5 if he buys 150 such articles.
72 articles for --> $82.80
1 article for - - - > 82.80/72
150 articles for --> (82.80/72)*150
= $172.5
Answer:
$172.5
Step-by-step explanation:
Given:
Shopkeeper buys = 72 articles
Price = $ 82.8
To Find:
The amount he'll need to pay If he buys 150 articles.
Solution:
Amount if he buys 150 articles
[tex] \boxed{\rm \: No. \: of \: articles \: he \:will \: buy × \cfrac{Cost \: of \: that \: article \: he \: has}{Number \: of \: articles \: he \: has}} [/tex]
[tex] = \$ \bigg(\rm150 * \cfrac{82.80}{72}\bigg) [/tex]
[tex]= \$ (150* 1.15)[/tex]
[tex] = \$172.5[/tex]
So we can conclude that:
$172.5 he will have to pay if he buys 150 such articles.
Determine the equation of the line with slope m=2/3, passing through the point (0,4)
Answer:
y = 2/3x + 4
Step-by-step explanation:
The slope-intercept form is y=mx+b. m (the slope) is equal to 2/3, so you can substitute that number in for m. B is the y value of the y-intercept. The y-intercept is (0,4) as given in the problem, so the value of b is 4. You can substitute that value into the equation as well.