Answer:
Son's age is 25.
Step-by-step explanation:
Let the Father's age be 2x.
Let the son's age be x.
Five years ago:
Man's age will be = 2x - 5
Son's age will be = x - 5
If the ratio of their ages five years ago was 9:4, then:
2x - 5/x-5 = 9/4
⇒ 4(2x - 5) = 9(x - 5)
⇒ 8x - 20 = 9x - 45
⇒ -20 + 45 = 9x - 8x
⇒ 25 = x
∴ x = 25
Hence, the son's age = 25 years
If x = 25, the father's age (2x) will be 2 × 25 = 50 years
What is the equation of the line that passes through the given point and is perpendicular to the given line?
Point: (1,1)
Line: y=15x+45
Answer:
y= -1/15x + 16/15
Step-by-step explanation:
When two lines are perpendicular to each other that means their slopes are the negative reciprocals of each other.
So that means if a line has has a slope of 6, a line perpendicular to that line will have a slope of -1/6.
(a reciprocal is when the fraction is flipped over)
In this case, the negative reciprocal of 15 would be -1/15. So the slope of the line that is perpendicular would be -1/15.
The equation we would have so far for that line would be: y=-1/15x+b
Now we have to find the 'b' or the y intercept, which we can get by plugging in the point that was given (1,1), which is on that line.
Which gives us 1=-1/15(1)+b.
1=-1/15+b
1+1/15=b
Then you solve for b and get b= 16/15.
The equation of the line that is perpendicular to the given line is y= -1/15x + 16/15.
The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is
y = 15x - 14.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Let the equation of a line is y = mx + c.
The line is perpendicular to y = 15x + 45.
y = 15x + 45 is in the form of y = mx + c
This means,
Slope = 15
m = 15
The line passes through the point (1, 1) = (x, y).
This means,
y = mx + c
1 = 15 x 1 + c
1 = 15 + c
c = 1 - 15
c = -14
The equation of the line is y = 15x - 14.
Thus,
The equation of the line that passes through the point (1, 1) and is perpendicular to y = 15x + 45 is
y = 15x - 14.
Learn more about equation of a line here:
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Help multiple choice
Answer:
the first one
Step-by-step explanation:
evaluate log25+log8 _log2
Step-by-step explanation:
log 25 + log 8 = log (25 × 8) = log 200
log 200 - log 2 = log (200 ÷ 2) = log 100
logarithm base 10 of 100 is 2.
If < W and < Y are supplementary, and < W = 121 °, then what would < Y measure?
Select one:
a. 121 °
b. 69 °
c. 59 °
d. 13 °
Answer:
Option c. 59°
Step-by-step explanation:
<W+<Y=180
121+<Y=180
<Y=180-121
<Y=59
Answered by GAUTHMATH
Tap on the picture! Needing help ASAP please♥️
Step-by-step explanation:
everything can be found in the picture
WRITE THE FUNCTION FOR THE GIVEN TABLE PLS
Answer:
y=X²-4x+5
Step-by-step explanation:
substitute all the left side values to get the outputs..
y=(5)²-4(5)+5 =10
Answer:
A
Step-by-step explanation:
In fact, if we try to substitute, we have:
10 = 5^2 -4(5) +5
10 = 25 - 20 + 5
10 = 10 (ok)
17 = -2^2 - 4(-2) + 5
17 = 4 + 8 + 5
17 = 17 (ok)
and so on
Help me solve this problem please
Answer:
A 2,3,6 :)
Step-by-step explanation:
thats answer corect me if im wrong hope it help
amy is walking laps whilst frank is jogging laps on the nature trail. Amy completes a lap in 15 minutes, frank completes a lap in 6 minutes. How long will it take before they both finish at the same time
Answer:
9 minutes
Step-by-step explanation:
Firstly they were in the same pace, Amy was walking while Frank was jogging.
then it will be 15 - 6 = 9
¿Cuántos números distintos pueden formarse con los dígitos 4, 5, 6 y 7 sin repetir ninguno de ellos?
Answer:
24.
Step-by-step explanation:
Para determinar cuántos números distintos pueden formarse con los dígitos 4, 5, 6 y 7 sin repetir ninguno de ellos se debe realizar el siguiente cálculo:
4, 5, 6 y 7 = 4 números
4 x 3 x 2 x 1 = X
12 x 2 = X
24 = X
Por lo tanto, con los dígitos 4, 5, 6 y 7 pueden formarse 24 números.
A restaurant owner is planning to have a courtyard area sodded. The sod comes in rolls that are 3 feet long by 1 foot wide. If the courtyard measures 60 feet by 50 feet, which of the following expressions represents the number of rolls of sod needed?
Answer:
[tex](60\times 50)\div 3[/tex]
Step-by-step explanation:
We are given that
Length of roll of sod, l=3 feet
Width of roll of sod, b=1 feet
Length of courtyard, L=60 feet
Breadth of courtyard, B=50 feet
Area of rectangle=[tex]Length\times breadth[/tex]
Using the formula
Area of roll of sod=[tex]3\times 1 feet^2[/tex]
Area of roll of sod=3 square feet
Area of courtyard=[tex]60\times 50[/tex] square feet
Number of rolls of sod needed=[tex]\frac{Area\;of\;courtyard}{area\;of\;roll\;of\;sod}[/tex]
Using the formula
Number of rolls of sod needed=[tex]\frac{60\times 50}{3}[/tex]
Number of rolls of sod needed=[tex](60\times 50)\div 3[/tex]
This is required expression which represents the number of rolls of sod needed.
What percent of the trees sampled were less than 75 ft tall?
Answer:
D
Step-by-step explanation:
Answer:
B=45
Step-by-step explanation:
Express 28 as the sum of three prime numbers
a) 3, 11 and 13
b) 5, 11 and 13
c) 2, 7 and 19
d) 2, 5 and 13
Answer:
a
Step-by-step explanation:
because is a ok yo12222122221112w
Answer:
Option C is correct
Step-by-step explanation:
[tex]3 + 11 + 13 = 27[/tex]
[tex]5 + 11 + 13 = 29[/tex]
[tex]2 + 7 + 19 = 28[/tex]
[tex] 2 + 5 + 13 = 20[/tex]
Hope it is helpful....Please help SUMMER SCHOOL
Question
(what are the slope and the y-intercept of the line shown in the graph)
simplify(x_2y)(x_2y)_(x+2y)(x+2y)
Answer:
-8xy
Step-by-step explanation:
Expand
( x − 2 y ) ( x − 2 y )
x ⋅ x + x ( − 2 y ) − 2 yx − 2 y ( − 2 y ) − ( x+ 2 y ) ( x + 2 y )
x2−4xy+4y2−(x+2y)(x+2y)
x2−4xy+4y2+(−x−(2y))(x+2y)
Multiply2by−1.x2−4xy+4y2+(−x−2y)(x+2y)
x2−4xy+4y2−x⋅x−x(2y)−2yx−2y(2y)
x2−4xy+4y2−x2−4xy−4y2
− 8xy
A client has two refrigerators, one in the kitchen and one in the basement.The former is new and efficient. The latter is 30 years old and uses 120Kwh/month. If this client pays 0.15/kwh
Incomplete question: we assume figures to explain further
Answer and explanation:
Given that client pays $0.15/kwh
If old fridge is inefficient and consumes 120kwh/month
And new fridge is efficient and therefore consumes 50kwh/month
For the old fridge, client will be paying
120×0.15= $18 per month on electricity charges
For the new fridge, client will be paying
50×0.15= $7.5 per month on electricity charges
Johan published a monthly poetry magazine. In March he printed 1400 copies of magazine. In April he increased his print run by 15%
Answer:
1610
Step-by-step explanation:
Answer:
1610
Step-by-step explanation:
you can easily get the solution without a calculator:
1400
+ 140 (+10%)
+ 70 (+5%)
= 1400 + 210
Mr. Tanaka is making Miso soup for his family. The recipe calls for 350 ml of Dashi. Mr. Tanaka plans to make a smaller batch using 280 ml of dashi. He wants to know what percent of the stock he will use compared to the original recipe. PLSS HELPPPPPPP Quick
What is the 10th term of the geometric sequence a(n)=-3(2)^(x-1_())
[tex]\displaystyle\ a(n)=-3(2)^ {n-1}\Longrightarrow a(10)=-3(2)^{10-1}=2^9\cdot -3=\boxed{-1536}[/tex]
Determine the axis of symmetry of the parabola with x-intercepts at (4, 0) and (12, 0)
Step-by-step explanation:
hope it helps thank you❤
6. Don Juan compro un terreno con las dimensiones que se muestran en la figura el cual se va acondicionar para realizar eventos sociales, por lo que desea instalar césped en la region sombreada. ¿Cuantos metros cuadrados de césped requiere? Considera rt=3.14 16 m O 50 24 m2 0 205 76 m2 256 00 m2 0 5504 m2
Answer:
Not sure but I think it might be A
Step-by-step explanation:
Took the test
Seriouslyy need help on this real answers only!
Answer:
C
Step-by-step explanation:
h(8) is given so D can't be true and A and B do not follow the domain and range restrictions
Find the value of each variable.
4V3
b
60°
45°
C
d
Answer:
a = 6, b = 6√2, c = 2√3, d = 6
Step-by-step explanation:
Applying,
sin60° = a/4√3
Therefore,
a = sin60°×4√3
a = (√3/2)(4√3)
a = 3×2
a = 6
Also,
cos60 = c/4√3
c = cos60×4√3
c = 0.5×4√3
c = 2√3
also,
tan45 = a/d
d = a/tan45
d = 6/(1)
d = 6
Also,
sin45 = a/b
b = a/sin45
b = 6/(1/√2)
b = 6√2
Over what interval is the parabola below decreasing?
A normal distribution has \mu = 65 and \sigma = 10. Find the probability that the average score of a group of n = 4 people is between 70 and 75 (both limits included).
Answer:
The probability that the average score of a group of n = 4 people is between 70 and 75=0.13591
Step-by-step explanation:
We are given that
[tex]\mu=65[/tex]
[tex]\sigma=10[/tex]
n=4
We have to find the probability that the average score of a group of n = 4 people is between 70 and 75.
[tex]P(70<\bar{x}<75)=P(\frac{70-65}{\frac{10}{\sqrt{4}}}<\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{75-65}{\frac{10}{\sqrt{4}}})[/tex]
[tex]=P(\frac{5}{5}<Z<\frac{10}{5})[/tex]
[tex]=P(1<Z<2)[/tex]
[tex]=P(Z<2)-P(Z<1)[/tex]
[tex]=0.97725-0.84134[/tex]
[tex]=0.13591[/tex]
Hence, the probability that the average score of a group of n = 4 people is between 70 and 75=0.13591
2x^2 - 4x + 5 x = -3
Dan invests £13000 into his bank account. He receives 4.7% per year simple interest. How much will Dan have after 6 years? Give your answer to the nearest penny where appropriate.
Step-by-step explanation:
SI = PxTxR/100
SI= (13000)(6)(4.7)/100
SI = 366600/100
SI= 3666
8,X,20 are in arithmetic progression,find the value of "x".
Answer:
x = 14
Step-by-step explanation:
Since the terns form an arithmetic progression then they have a common difference d , that is
a₂ - a₁ = a₃ - a₂
x - 8 = 20 - x ( add x to both sides )
2x - 8 = 20 ( add 8 to both sides )
2x = 28 ( divide both sides by 2 )
x = 14
Which polynomial function has x-intercepts –1, 0, and 2 and passes through the point (1, –6)
Answer:
y=3x(x+1)(x-2)=3x^3-3x^2-6x
Step-by-step explanation:
The polynomial function can be written in the form:
y=a(x-x1)(x-x2)(x-x3)
where
x1=-1
x2=0
x3=2
Therefore
y=a(x+1)(x-0)(x-2)=a(x^2+x)(x-2)=a(x^3-x^2-2x)
To find the value for "a" we use the info about the line passing in (1,-6):
-6=a(1-1-2)
a=3
y=3x(x+1)(x-2)=3x^3-3x^2-6x
Answer:
f(x) = 3x3 - 3x2 - 6x
Good luck! :D
Step-by-step explanation:
e) (x + 1)/(2x ^ 3 - 4x ^ 3) + (x - 1)/(2x ^ 3 + 4x ^ 2) = 1/(x ^ 2 - 4)
Answer:
X= − x ^3 + 2 x^2 − 3 x − 2 x ^3 ( x + 2 ) ( x − 2 ) = 0
Step-by-step explanation:
Iliana rotated trapezoid WXYZ 180° about the origin.
On a coordinate plane, trapezoid W X Y Z has points (negative 4, 2), (negative 3, 4), (negative 1, 4), (0, 2).
What is the correct set of image points for trapezoid W’X’Y’Z’?
W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
W’(4, 2), X’(3, 4), Y’(1, 4), Z’(0, 2)
W’(–2, –4), X’(–4, –3), Y’(–4, –1), Z’(–2, 0)
W’(2, 4), X’(4, 3), Y’(4, 1), Z’(2, 0)
Answer:
W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)
Step-by-step explanation:
The vertices of the trapezoid WXYZ are, W(-4, 2), X(-3, 4), Y(-1, 4), and Z(0, 2)
The coordinates of the image following the rotation transformation of the preimage (x, y) 180° about the origin is (-x, -y)
Therefore, following the rotation transformation of trapezoid WXYZ, the coordinates of the image W'X'Y'Z' are given as follows;
W(-4, 2) rotated 180° about the origin gives W'(4, -2)
X(-3, 4) rotated 180° about the origin gives X'(3, -4)
Y(-1, 4) rotated 180° about the origin gives Y'(1, -4)
Z(0, 2) rotated 180° about the origin gives Z'(0, -2)
Therefore, we get;
W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2).
Answer:
Its A
Step-by-step explanation:
i just took the test.
