Abram completes one lap of a go-cart track every 40 seconds. Joshua completes one lap of the same track every 30 seconds. Suppose Abram and Joshua cross the starting line at the same time.
a. How many seconds will pass before they cross the starting line at the same time again?
b. How many laps will Abram have completed in that time?
c. How many laps will Joshua have completed in that time?
Answer:
Below in bold.
Step-by-step explanation:
a. This is the Lowest common multiple of 30 and 40 which is
120 seconds.
b. In 120 seconds Abram had completed 120/40
= 3 laps.
c. Joshua completed 120/30 = 4 laps.
Answer:
Step-by-step explanation:
A, Lowest common mutiple of 30 and un is 120 seconds
(40x3 = 120, 30x4 = 120)
6.120/40 = 3 laPs Abram did 3 laps.
L. 120/30 = u laPs Jeshya did u laps
What is the value of c
Answer:
if im not mistaken its 121
Step-by-step explanation:
Answer:
99°
Step-by-step explanation:
The interior angle sum of any 5 sided polygon is 540°.
540-53 = 487 - 137 = 350 - 105 = 245- 146 = 99°
Which of the following best describes a basic postulate of Euclidean
geometry?
A. All circles measure 360°
B. All right triangles are congruent.
C. A straight line segment has a midpoint.
D. A straight line segment can be drawn between any two points.
Answer:
D. A straight line segment can be drawn between any two points.
Step-by-step explanation:
Euclid of Alexandria was famously known and regarded as the founder of geometry, as well as the father of geometry. He was born in the Mid-fourth century, BC and he specialized in the field of Mathematics. Some of his popular works in the field of Mathematics were Euclid's Elements, Euclidean algorithm and Euclidean geometry.
One of the basic postulate of Euclidean geometry is that a straight line segment can be drawn between any two points.
Others include;
I. All right angles are congruent.
II. All straight line segment is indefinitely extendable in a straight line.
What is the inverse of the function () 2x 10?
Answer:
I assume that we want to find the inverse of the function:
f(x) = 2*x + 10
Remember that the inverse of a function f(x), is a function g(x) such that:
f( g(x) ) = g( f(x) ) = x
Because f(x) is a linear function, we can assume that g(x) will also be a linear function:
g(x) = a*x + b
let's find the values of a and b.
We will have that:
f( g(x) ) = 2*g(x) + 10 = 2*(a*x + b) + 10
And that must be equal to x, then we need to solve:
2*(a*x + b) + 10 = x
2*a*x + 2*b + 10 = x
this must be true for all values of x, so we can separate it as:
(2*a*x) + (2*b + 10) = x + 0
2*a*x = x (one equation for the terms with x)
2*b + 10 = 0
Solving these two equations we get:
2*b = -10
b = -10/2 = -5
2*a*x = x
2*a = 1
a = 1/2
Then the inverse function is:
g(x) = (1/2)*x - 5
How do i get X? i cant quite figure it out
Answer:
x is 90° I hope it will help you please follow me
Answer:
My answer came 78°
Step-by-step explanation:
First, B and C are alternate angles so,
71°= y (let) + 29°
Y= 42°
Then, X + 42 + 60 = 180°
X = 180 - 102
X = 78 °
Hope this helps. :)
Help urgent In a class of 35 students 15 of them have cats 16 have dogs 3 hangs none how many probability does have both
Answer:
9/25
Step-by-step explanation:
Number of student who has cat , dog = 25 - 3 = 22
Number of students who has cat and dogs = (15 + 16) - 22
= 31 - 22 = 9
Number of students who has only cats = 15 - 9 = 6
Number of students who has only dogs = 16 - 9 = 7
P(Cat & dog) = 9/25
choose the equation that satisfies the data in the table
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
See this attachment
option D is correctif the mean of x1,x2,x3 and x4 is 6 then find the mean of x1+10,x2+8,x3+16 and x4+2
Answer:
f the mean of this set is equal to 20, we can write down the below equation,
20 = (x1 + x2 +x3 + .... + x10)/10
x1 + x2 + x3 + ... x10 = 200
Then we can also write an equation for the mean of the given numbers as below,
Mean = [(x1+4) + (x2+8) + (x3+12) + .... + (x10+40)]/10
= (x1 + x2 + x3 + ... + x10 + 4 + 8 + 12 + ... + 40)/10
Then we can use above equation (1) to replace x1 + x2 + x3 + ... + x10 by 200
Mean = (200 + 4 + 8 +12 + 16 + 20 + 24 + 28 + 32 + 36 + 40)/10
= 420/10
= 42
If you remember Arithmetic Progressions you can simply add together the above number set.
If you closely look above, you can find that there is an Arithmetic Progression : 4, 8, 12, ... , 40
Here we want the addition of 10 terms. So we can use,
Sn = n/2(a+l)
S10 = 10/2(4+40)
= 220
Then you can easily get the answer,
Mean = (200 + 220)/10
= 42
Factor the polynomial function over the complex numbers.
f(x)=x^3+2x^2+5x+10
Answer:
[tex]{ \tt{f(x) = (x + 2)(x + 2.2i)(x - 2.2i)}}[/tex]
find the value of the unknown.
Answer:
86.5
[tex]14 + 8 + 12.5 = 34.5 \: \: 121 - 34.5 = 86.5[/tex]
99, 159, 219, ___. To find the next number after 219, we should a. Add 69 to 219 b. Subtract 60 from 219 c. Add 60 to 219 d. Add 40 to 219
Answer:
C
Step-by-step explanation:
99+60=159.
159+60=219
219+60=279
What are angles a,b and c
Answer:
A=38°
B=84°
C=68will use the property of an isosceles triangle to find the answer
A polynomial p has zeros when x = -2, x = 1/3, and x =3.
What could be the equation of p? Choose 1 answer:
a. p(x) = (x + 2)(x + 3)(3x + 1)
b. p(x) = (x + 2)(x + 3) (3x - 1)
C. p(x) = (x + 2)(x - 3)(3x - 1)
D. p(x) = (x - 2)(x + )(3x + 1)
Answer:
p(x) = ( x +2) (3x - 1) ( x-3)
Step-by-step explanation:
We know the equation for a polynomial with given zeros is
f(x) = a(x-b1) (x-b2)...... where b are the zeros and a is a constant
Since the zeros are x = -2, x = 1/3, and x =3.
p(x) = a( x - -2) (x - 1/3) ( x-3)
p(x) = a( x +2) (x - 1/3) ( x-3)
We can pick the value of a since we are not given a point on the function. Pick a=3
p(x) = 3( x +2) (x - 1/3) ( x-3)
Rewriting the second term
p(x) = ( x +2) (3x - 1) ( x-3)
please help me for this
What is this equation rewritten in logarithmic form?
9X = 3
A. log 3 = x
B. log, 3 = 9
C. log3 9 = x
D. log3 x = 9
Answer:
A. log9 3=x
Step-by-step explanation:
The logarithmic form with base 9 is log₉ 3 = x.
The correct option is A.
The equation 9ˣ = 3 can be rewritten in logarithmic form by identifying the base and the result of the exponential operation. In this case, the base is 9, the result is 3, and the exponent is x.
The logarithmic form with base 9 is log₉ 3 = x.
Option A, log₉ 3 = x, is the correct representation of the equation in logarithmic form.
The logarithmic form states that the logarithm of a number (3 in this case) to a specific base (9 in this case) is equal to the exponent (x in this case).
In the equation, 9ˣ = 3, the logarithmic form log₉ 3 = x indicates that the logarithm of 3 with base 9 is equal to x. This means that 3 is the result of raising 9 to the power of x.
Therefore, option A, log₉ 3 = x, is the correct answer representing the equation 9ˣ = 3 in logarithmic form.
To learn more about the logarithms;
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The population of a town is 157,220 and is decreasing at a rate of 0.8% each year. Predict the population in 5 years (round to the nearest whole number).
Answer:
151,031
Step-by-step explanation:
If the population of a town is decreasing at 0.8% each year, the new population of the town will be [tex]100\%-0.8\%=99.2\%[/tex] of what it was last year. To find 99.2% of something, multiply it by 0.992. Therefore, we can write the following equation:
[tex]f(x)=157,220\cdot 0.992^x[/tex], where [tex]f(x)[/tex] is the population of the town [tex]x[/tex] years after the town had a population of 157,220.
Substitute [tex]x=5[/tex] into this equation to get the projected population after 5 years:
[tex]f(5)=157,220\cdot 0.992^5, \\f(5)=151031.019048,\\f(5)\approx \boxed{151,031}[/tex]
Therefore, in 5 years, the population should be 151,031.
Solve (−3) ⋅ 2
please help
Answer:
-6
Step-by-step explanation:
3*2=6
so the opposite of 6 is -6
Also a negetive times a positive is always a negetive number
PLEASE HELP!! would this be symmetric or reflexive property?
Answer: It's "reflexive" because the equation is equal on both sides
Step-by-step explanation: The reason it isn't symmetric property, is because the variables are mismatched (it's not the same on both sides.)
Hope this helped!!
I needddd help it’s urgenttttt!!!!
Help would be greatly appreciated
Answer:2/pi
Step-by-step explanation:
First, name the points. Top Left will be A, Top Right will be B, Bottom Right will be C, and Bottom Left will be D. Now, the area of ABCD is 4. Then, we have to find the area of the circle. The center to the midpoint of AB is 1. The length of the midpoint of AB to B is 1. So, using the Pythagorean Theorem, it will be 1^2 + 1^2 = 2, then it will be sqrt2. Finding the area of the circle will be easy now that we have the radius. sqrt2*sqrt2*pi = 2pi. So, it will be 4/2pi, and simplified, it will be 2/pi.
The mass of 5 m' of copper is 44 800 kg. Work out
the density of copper.
6) Given that the point (3, −10) lies on the graph of a function , what point must be on the graph of ℎ
where ℎ() = ( − 4) + 2?
Answer:
(7,-8)
Step-by-step explanation:
Given
(x,y) = (3,-10)
Required
The equivalent point on h(x) = k(x - 4) + 2
(x,y) = (3,-10) means
k(3) = -10
Substitute 7 for x in h(x)
h(7) = k(7-4) + 2
h(7) = k(3) + 2
Substitute -10 for k(3)
h(7) = -10 + 2
h(7) = -8
So, the equivalent point on h(x) is
(7,-8)
solve the formula for a
(q&c in picture)
Answer:
C
Step-by-step explanation:
Subtract Vot from the given equation
s - Vo*t = 1/2 a t^2 Multiply by 2
2(s - Vo*t) = at^2 Divide by t^2
2(s - Vo*t) / t^2 = a
Looks like C is the answer.
Choose the graph that correctly corresponds to the equation y = −4
Answer:
e
Step-by-step explanation:
the graph should look something like this
Sam buys a carpet for his apartment. The diagonal length of the carpet is 12 feet and the width is 10 feet. Find the length of the carpet.
Answer: 6.633 Feet
Step-by-step explanation:
Who can help me with problem 2 you can earn 11 points
Answer:
m∠ADC = 90°
5x-5 = 90
x = 19
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the area of the base is 12.5 ft ^2 12.5 ft
2
and the height of the pyramid is 16 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
833.3 ft^3
Step-by-step explanation:
The formula for the volume of a pyramid is:
V = (lwh)/3
V = volume
l = length of base
w = width of base
h = height of pyramid
Now we just correspond the values with the variables:
l = 12.5
w = 12.5
h = 16
And plug these values into the formula:
((12.5)(12.5)(16))/3
((156.25)(16))/3
2500/3
833.3 ft^3
Hope this helps (●'◡'●)
The solution is : the volume of a pyramid with a square base is 833.3 ft^3.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
we know that,
The formula for the volume of a pyramid is:
V = (lwh)/3
V = volume
l = length of base
w = width of base
h = height of pyramid
Now we just correspond the values with the variables:
l = 12.5
w = 12.5
h = 16
And plug these values into the formula:
=((12.5)(12.5)(16))/3
=((156.25)(16))/3
=2500/3
=833.3 ft^3
Hence, The solution is : the volume of a pyramid with a square base is 833.3 ft^3.
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The formula for centripetal acceleration, a, is given by this formula, where v is the velocity of the object and r is the object's distance from the center of the circular path: . Solve the formula for r.
Answer:
v = √ar
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION;
The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distance from the center of the circular path. Solve the formula for the velocity. the formula is a= v^2/ r
the given formula is (a= v^2/ r) .....eqn(1)
Where
a=centripetal acceleration
r = object's distance
We were told to find velocity (v)
From eqn(1) we can cross multiply, then we have
a.r=v^2 ...................eqn(2)
Then we can make (v^2) the subject of the formula, we have
(v^2) = ar
We can make "v" subject of the formula, then we have
v = √ a*r
Answer:
r = v^2/a
Step-by-step explanation:
square of (1\4A+1\4B)^2
Answer:4a = 2⋅(2a)⋅1 4 a = 2 ⋅ ( 2 a) ⋅ 1
Step-by-step explanation:
Factor 4a^2-4a+1. 4a2 − 4a + 1 4 a 2 - 4 a + 1. Rewrite 4a2 4 a 2 as (2a)2 ( 2 a) 2. (2a)2 − 4a+1 ( 2 a) 2 - 4 a + 1. Rewrite 1 1 as 12 1 2. (2a)2 − 4a+12 ( 2 a) 2 - 4 a + 1 2. Check that the middle term is two times the product of the numbers being squared in the first term and third term. 4a = 2⋅(2a)⋅1 4 a = 2 ⋅ ( 2 a) ⋅ 1.
A shopkeeper allows 15% discount on the marked price, still he manages to have 7% profit. How much high did he mark his goods above the cost price?
Answer: [tex]25.9\%[/tex]
Step-by-step explanation:
Given
Shopkeeper allows 15% discount on the marked price and still manages a profit of 7%
Suppose the marked price is [tex]x[/tex]
So, the selling price is [tex](1-0.15)x=0.85x[/tex]
Suppose the cost price is [tex]y[/tex]
[tex]\Rightarrow \dfrac{0.85x-y}{y}=7\%\\\\\Rightarrow \dfrac{0.85x}{y}-1=0.07\\\\\Rightarrow \dfrac{0.85x}{y}=1.07\\\\\Rightarrow y=\dfrac{0.85x}{1.07}\\\\\Rightarrow y=0.794x[/tex]
So, the percentage the shopkeeper marked his goods above cost price
[tex]\Rightarrow \dfrac{x-y}{y}\times 100\\\\\Rightarrow \dfrac{x-0.794x}{0.794}\times 100\\\\\Rightarrow \dfrac{0.2056}{0.794x}\times 100\\\\\Rightarrow 25.89\%\approx 25.9\%[/tex]
