Answers
Answer:
1. Steve's age is 18 and Anne's age is 8.
2. Max's age is 17 and Bert's age is 11.
3. Sury's age is 19 and Billy's age is 9.
4. The man's age is 30 and his son's age is 10.
Step-by-step explanation:
1. Let us assume that:
S = Steve's age now
A = Anne's age now
Therefore, in four years, we have:
S + 4 = (A + 4)2 - 2
S + 4 = 2A + 8 - 2
S + 4 = 2A + 6 .................. (1)
Three years ago, we have:
S - 3 = (A - 3)3
S - 3 = 3A - 9 ................................ (2)
From equation (2), we have:
S = 3A - 9 + 3
S = 3A – 6 …………. (3)
Substitute S from equation (3) into equation (1) and solve for A, we have:
3A – 6 + 4 = 2A + 6
3A – 2A = 6 + 6 – 4
A = 8
Substitute A = 8 into equation (3), we have:
S = (3 * 8) – 6
S = 24 – 6
S = 18
Therefore, Steve's age is 18 while Anne's age is 8.
2. Let us assume that:
M = Max's age now
B = Bert's age now
Therefore, five years ago, we have:
M - 5 = (B - 5)2
M - 5 = 2B - 10 .......................... (4)
A year from now, we have:
(M + 1) + (B + 1) = 30
M + 1 + B + 1 = 30
M + B + 2 = 30 .......................... (5)
From equation (5), we have:
M = 30 – 2 – B
M = 28 – B …………………… (6)
Substitute M from equation (6) into equation (4) and solve for B, we have:
28 – B – 5 = 2B – 10
28 – 5 + 10 = 2B + B
33 = 3B
B = 33 / 3
B = 11
Substituting B = 11 into equation (6), we have:
M = 28 – 11
M = 17
Therefore, Max's age is 17 while Bert's age is 11.
3. Let us assume that:
S = Sury's age now
B = Billy's age now
Therefore, now, we have:
S = B + 10 ................................ (7)
Next year, we have:
S + 1 = (B + 1)2
S + 1 = 2B + 2 .......................... (8)
Substituting S from equation (7) into equation (8) and solve for B, we have:
B + 10 + 1 = 2B + 2
10 + 1 – 2 = 2B – B
B = 9
Substituting B = 9 into equation (7), we have:
S = 9 + 10
S = 19
Therefore, Sury's age is 19 while Billy's age is 9.
4. Let us assume that:
M = The man's age now
S = His son's age now
Therefore, now, we have:
M = 3S ................................... (9)
Five years ago, we have:
M - 5 = (S - 5)5
M - 5 = 5S - 25 ................ (10)
Substituting M from equation (9) into equation (10) and solve for S, we have:
3S - 5 = 5S – 25
3S – 5S = - 25 + 5
-2S = - 20
S = -20 / -2
S = 10
Substituting S = 10 into equation (9), we have:
M = 3 * 10
M = 30
Therefore, the man's age is 30 and his son's age is 10.
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Answers
Answer:
hello your question lacks the required options but i will provide a general answer to your question
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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——————————-
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Answers
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
anyway
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Answers
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Answers
Answer:
22.5 feet
Step-by-step explanation:
set up a proportion, then cross-multiply
18/20 = x/25 or 18/x = 20/25
The height of the tree is 22.5 ft
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given that, the height to the top of a flagpole is 18 feet, the flagpole casts a shadow of 20 feet, and a tree casts a shadow of 25 feet.
Here we need to find the height of the tree,
We will use the concept of the similar triangles to find the same,
Let the height of the tree be x
So. according to the definition of similar triangles,
18 / 20 = x / 25
x = 45 / 2
x = 22.5
Hence, the height of the tree is 22.5 ft
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A line includes the points (-8,8) and (6,4). Select the correct point slope form equations of this line. (Remember there can be more than one)
Group of answer choices
y-8=(-2/7)(x+8)
y+8=(-2/7)(x-8)
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Answers
Answer:
y-8=(-2/7)(x+8) and y-4=(-2/7)(x-6)
Step-by-step explanation:
Point slope form equation: y - y₁ = m(x - x₁)
m is the same for all your answer choices, so you can disregard that part.
First point: (-8,8)
x₁ = -8; y₁ = 8
Plug those values into the point slope form equation and you get:
y-8=(-2/7)(x+8)
Do the same for the second point, and you get:
y-4=(-2/7)(x-6)
Answer:
first and third options
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope- formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 8, 8) and (x₂, y₂ ) = (6, 4)
m = [tex]\frac{4-8}{6+8}[/tex] = [tex]\frac{-4}{14}[/tex] = - [tex]\frac{2}{7}[/tex]
using (a, b ) = (- 8, 8 ), then
y - 8 = - [tex]\frac{2}{7}[/tex] (x - (- 8) ) , that is
y - 8 = - [tex]\frac{2}{7}[/tex](x + 8) ← first option
using (a, b ) = (6, 4 ), then
y - 4 = - [tex]\frac{2}{7}[/tex] (x - 6) ← third option
Problem: According www.textrequest, an American between 18-24 sends and receives about 128 text messages per day. Assume that the population standard deviation is 30 for this age group. To get an idea about the true population mean you take a survey of 100 adults in that age group and find that their average is 135. Create a 90% confidence interval for the population average for this age group.
Answers
Answer:
(130.08, 139.92)
Step-by-step explanation:
Given that:
Mean (m) = 135
Standard deviation (σ) = 30
Sample size (n) = 100
α = 90%
The confidence interval value is obtained using the relation:
Mean ± Zcritical * (standard deviation / sqrt(n))
Zcritical at 90% = 1.64
standard deviation / sqrt(n) = 30 / sqrt(100)
= 30 / 10 = 3
Hence,
135 ± 1.64 * (3)
Lower limit : 135 - (1.64 * 3) = 130.08
Upper limit : 135 + (1.64 * 3) = 139.92
Hence,
Confidence interval = (130.08, 139.92)
Carmen quiere invertir 700 dólares, de tal forma que en
90 días le produzca 63 dólares de interés simple.
¿Que tasa de interés debe elegir?
Answers
La fórmula de interés simple, nos permite calcular I, que es el interés ganado o pagado de un préstamo. Según esta fórmula, la cantidad de interés está dada por I = C·i·t, donde C es el capital, i es la tasa de interés anual en forma decimal, y t es el período de tiempo expresado en años Tenemos que:
C = 700 dólares
i = ???
t = 90/360 = 0.25 (Expresado en años)
I = C*i * t
i = I / C*t
i = 63/ (0.25*700)
i = 0.36
R/ Debe elegir una tasa de interés de 36% anual.
The interest on the amount invested for 90days given $63 as interest is 36.5%
Simple interest is the amount of money added to money invested. It is calculated as:
[tex]SI = \frac{PRT}{100}[/tex]
P is the amount invested (principal) = $700
R is the rate
T is the time (in years) = 90/365
SI is the interest = $63
Substitute the given values into the formula
[tex]63=\frac{700 \times R \times 90}{365 \times 100}\\63=\frac{63000R}{36500}\\63= 1.72602R\\R=36.5\%[/tex]
This shows that the interest on the amount invested for 90days given $63 as interest is 36.5%
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Which expression is equivalent to 8x - 12y + 32?
A. 16(0.5x - 4y + 32)
B. 16(0.5x - 0.75y + 2)
C. 16(0.5x - 0.75 + 32)
D. 16(0.5x + 4y +2
Answers
Answer: B
Step-by-step explanation:
It’s the only one that makes sense.