The force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.
According to the question,
We have the following information:
The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. And when m=8kg and d=5meters then F=100 Newtons.
Now, let's take the constant for this case to be k.
We have the following expression:
F = km/[tex]d^{2}[/tex]
Putting the values in this expression to find the value of k:
100 = 8k/(5*5)
Using the cross multiplication method:
2500 = 8k
k = 2500/8
k = 312.5
Now, we have the following value of F:
F = 312.5*2/15*15
F = 625/225
F = 2.78 Newton
Hence, the force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.
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find the middle side of each triangle. round your answers to the nearest tenth if necessary.
Step-by-step explanation:
using Pythagoras theorem.
37,
x² = 6² + 8²
x = √6²+8² = 10ft
38.
13²=12²+x²
169 = 144 + x²
√169 - 144 = x = 5cm
hope it helps. :)
Answer:
x = 10 and x = 5
Step-by-step explanation:
using Pythagoras' identity
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
(36)
x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )
x = [tex]\sqrt{100}[/tex] = 10
(38)
13² = x² + 12²
169 = x² + 144 ( subtract 144 from both sides )
25 = x² ( take square root of both sides )
[tex]\sqrt{25}[/tex] = 5 = x
x = 5
Does the function y=x have an inverse? If so does it pass the horizontal line test?
Yes, y=x has an inverse.
Yes, y=x passes the horizontal line test.
If it didn't pass the horizontal line test, it would not have an inverse.
polynomial function
Answer: (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 )
Step-by-step explanation:
To write a polynomial in standard form, simplify and then arrange the terms in descending order. Expand (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 ) using the FOIL Method.
Which of the following represents the series?
–12 + (–5) + 2 + 9 + 16
sum from k equals 0 to 4 of negative 19 plus 7 times k
sum from k equals 1 to 5 of negative 19 minus 7 times k
sum from k equals 0 to 4 of negative 12 plus 7 times k
sum from k equals 1 to 5 of negative 12 minus 7 times k
(image includes proper visuals for each option)
The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;
[tex]\sum\limits_{k = 0}^4-12+7\cdot k[/tex]What is an arithmetic series?An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.
The series in the question is; -12 + (-5) + 2 + 9 + 16
Each term in the series is obtained from the previous term by the addition of a 7The series in therefore a series of an arithmetic sequence
The equation of the series when the first term is -12 can therefore be presented as follows;
-12 + 7·k
Where;
-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1
When n = 1, k = 0, which gives;When k = 0, the expression, -12 + 7·k = -12 + 7 × 0 = -12When k = 1, -12 + 7·k = -12 + 7 × 1 = -5When k = 2, -12 + 7·k = -12 + 7 × 2 = 2When k = 3, -12 + 7·k = -12 + 7 × 3 = 9When k = 4, -12 + 7·k = -12 + 7 × 4 = 16The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4
The expression that represents the series is therefore the option;
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Find the surface area and volume of each triangular prism (base is a right triangle).
triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft
The surface area of a triangular prism = 108cm2
The volume of the triangular prism = 48cm3
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
Given that
The Triangle legs are 3 and 4 feet long, the hypotenuse is 5 feet long, and the prism height is 8 feet tall.
We have to determine the surface area and volume of each triangular prism
here a = 3ft b = 4ft c = 5ft and height h = 8ft
Surface area of triangular prism = ab + h(a+b+c)
= 3x4 + 8(3+4+5)
= 12 + 8(12)
= 12 + 96
= 108cm2
Volume of triangular prism = ½(abh)
= ½ (3x4x8)
=1/2(96)
= 96/2
= 48cm3
Therefore
The surface area of a triangular prism = 108cm2
The volume of the triangular prism = 48cm3
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the 6th term of an arithmetic progreion i 35 and the 13th term i 77. find the 20th term
The 20th term of the given arithmetic progression is 119.
What is arithmetic progression?An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).
3,6,9,12,15,18, and 21 are A.P. examples.
So, the formula for the nth term:
a+(n-1)d, where d is the common difference
Now, take out the equation:
6th term = 35
a+(6-1)d= 35
a+5d=35 ....(1)
13th term = 77
a+12d= 77 .....(2)
Then, subtract equation (1) from equation (2):
a+12d-(a+5d)= 77-35
a+12d-a-5d= 42
7d=42
d=6
Calculate from equation (1):
a= 35-5d= 35-5(6)= 35-30 = 5
20th term= a+19d= 5+19(6)= 119
Therefore, the 20th term of the given arithmetic progression is 119.
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Wyatt says that both red lines are lines of symmetry. Is he correct? Why or why not?
Answer:
Step-by-step explanation:
There is only one line of symmetry:
because the one that is vertical is not representing symmetry.
HWLP ASPP PLEASE SHOW UR WORK
Answer: 1. 3
5. -3
Step-by-step explanation:
: in a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old?
the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243
the complete question is:
The demographic profile of Ecuador in 2018 is • 27.08% of the population are 0–14 years old • 18.35% are 15–24 years old • 39.59 are 25–54 years old • 7.53% are 55–64 years old • 7.45% are 65 years and older. In a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55–64 years old, 6 are 25–54 years old, 4 are 15–24 years old and 3 are 0–14 years old?
answer:
P(x) = P(x=2) + P(x=5) +p(x=6) +p(x=4) +p(x=3)
=20[tex]C_{2}[/tex][tex](7.45)^{2}[/tex][tex](2.55)^{18}[/tex]+20[tex]C_{5}[/tex][tex](7.53)^{5}[/tex][tex](2.47)^{15}[/tex]+20[tex]C_{6}[/tex][tex](39.59)^{6}[/tex][tex](0.41)^{14}[/tex]+20[tex]C_{4}[/tex][tex](18.35)^{4}[/tex][tex](1.65)^{16}[/tex]+20[tex]C_{3}[/tex][tex](27.08)^{3}[/tex][tex](2.92)^{17}[/tex]
P(x) = 0.2424
the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243
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algebra 2 please help :)!
Help please
I need this by tomorrow
Answer:
I hope this will help. Tip: reuse the formula!
PLEASE HELP, QUESTION IN THE PICTURE
Step-by-step explanation:
AC is the combination of AB and BC.
so, AB + BC = AC
(2n - 1) + (4n + 5) = 10n - 12
2n - 1 + 4n + 5 = 10n - 12
6n + 4 = 10n - 12
4 = 4n - 12
16 = 4n
n = 4
Please help F(-1/2)=1 and f(0)=-4
Question:
Write a linear function f with f (- 1/2) = 1 and f (0) = -4
The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4
Let the equation in variables x and y can be written in the form y = mx + c
So f (- 1/2) = 1
this gives, 1 = -1/2m+c -----------eq 1
Also f (0) = -4
This gives -4 = c. --------------eq2
Now Putting the value of c in the equation in eq1 we get m=0.
So 1 = -1/2m+c
1 = -1/2m - 4
m = -5
Then we get;
y = -5x -4.
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Callie has a rope that is 14.7 inches long. She cuts the rope into 3 pieces. If each piece is the same length, how long is each piece of rope?
Answer:
Each piece will be 4.9 inches long
Step-by-step explanation:
All you have to do is divide 14.7 by three as the rope itself is cut into 3 equal parts
therefore: 14.7/ 3= 4.9
what is the vertex of -2x^2 +12x -10
The vertex of the function f(x) = x^2 + 12x is (-6, -36).
How can the vertex be expressed?The concept that will be used here is the concept of Standard equation of a curve in vertex form.
The standard equation can be written as
f (x) = ax^2 + bx + c
Then the Vertex is the (h,k)
Then the X-coordinate of the vertex can be written as (h = -b/2a) where k = f(h)
If we compare the given equation with the standard form, then we have
a = 1, b = 12 and c = -10
Then we can input the values into the (h = -b/2a)
h =[ -12/2(1)] = - 6
Then we can substitute the value of h in f (x) which is f(x) = x2 + 12x
k = f(h)= f (-6) =[ (-6)2 + 12 (-6)]
= [36 - 72] = -36
In conclusion the vertex is (-6, -36).
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A family buys a studio apartment for 150,000. They pay a down payment of $22,500. a.Their down payment is what percent of the purchase price?
b. What percent of the purchase price would a $60,000 down payment be?
please help!!!
In the diagram below of triangle
F
G
H
FGH,
I
I is the midpoint of
F
H
‾
FH
and
J
J is the midpoint of
G
H
‾
GH
. If m
∠
H
F
G
=
57
−
6
x
∠HFG=57−6x, and m
∠
H
I
J
=
−
4
x
+
49
∠HIJ=−4x+49, what is the measure of
∠
H
I
J
∠HIJ
Applying the corresponding angles theorem, the measure of ∠HIJ = 33°.
What is the Corresponding Angles Theorem?If two triangles are similar to each other, their corresponding angles would be equal. Also, based on the corresponding angles theorem, corresponding angles are equal to each other.
Triangles IHJ and FGH are similar to each other, therefore, angles HFG and HIJ are corresponding angles.
Therefore:
The measure of angle HFG = the measure of angle HIJ
m∠HFG = 57 − 6x
m∠HIJ = −4x + 49
Thus:
57 − 6x = -4x + 49
Combine like terms
4x - 6x = -57 + 49
-2x = -8
Divide both sides by -2
-2x/-2 = -8/-2
x = 4
m∠HIJ = −4x + 49 = -4(4) + 49
m∠HIJ = 33°
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Complete Question:
In the diagram below of triangle FGH, I is the midpoint of FH and J is the midpoint of GH. If m∠HFG = 57 − 6x, and m∠HIJ = −4x + 49, what is the measure of ∠HIJ?
Image is the equation
Answer:
y = [tex]\frac{3}{4}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{3}{4}[/tex] , then
y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation
to find c substitute (- 4, 5 ) into the partial equation
5 = - 3 + c ⇒ c = 5 + 3 = 8
y = [tex]\frac{3}{4}[/tex] x + 8 ← equation of line
A cubic polynomial function f has a leading coefficient of 2 and a constant term of -5. When f(1) is zero and f(2) is three what is f(-5). Explain?
The value of f(-5) = -130
A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.
A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:
Ax3 + bx2 + cx +d = 0
For the given question the cubic equation will be:
2x3 + bx2 + cx - 5 = 0
Given
Leading coefficient (a) = 2
Constant (T) = -5
f(1) = 0
f(2) = 9
Therefore the equation formed will be:
2x3 + bx2 + cx - 5 = 0
Now f(1) = 0
2(1)3 + b(1)2 + c(1) - 5 = 0
2 + b + c -5 = 0
b + c = 3
b = 3-c -----(1)
On solving f(2) = 3
2(2)3 + b(2)2 + c(2) - 5 =3
16 + 4b + 2c – 5 =3
4b +2c = 3 – 11
4b + 2c = -8 ----(2)
Now substitute the b value in equation (2)
4(3-c) + 2c = -8
12 – 4c +2c = -8
-2c = -20
C =10
Now substitute the c value in equation (1)
b= 3 – c
b = 3 -10
b = -7
Now substitute the b and c values in the cubic equation
2x3 - 7x2 + 10x - 5 = 0
Now calculate f(-5)
2(-5)3 - 7(-5)2 + 10(-5) - 5
= -250 + 175 – 50 -5
= -130
Therefore the value of f(-5) = -130
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What is the answer to this question
Answer:
soda: 97
Hot dogs: 56
Step-by-step explanation:
S-sodas
H- hot dogs
S+H=153
41+H=S
Substitute equation
(41+H)+H=153
41+2H=153
-41. -41
2H=112
/2. /2
H=56
S+56=153
-56. -56
S=97
Hopes this helps please mark brainliest
Point B' is the image of point B after a reflection in a line. Write an equation of the line.
B(2, -4), B'(6, -4)
Answer:
x = 4
Step-by-step explanation:
what's the slope of 6x+13y= -18
Answer:
slope is the coefficient of x
so it is 6
good luck!!
if a farm has 30 chickens and cows and there are 82 chicken and cows legs all together then how many chickens and how many cows could the farm have?
Answer: 11 cows and 19 chickens
Step-by-step explanation:
Part A: Without calculating the values, compare the expressions using <, >, or =.
Write the correct symbol. Draw a model if it helps you.
(5+15)x13
31×(15+5)
The difference between 15 fours and
6 fours.
The sum of 4 fours and 5
fours
Part B: Explain how you compared the expressions without calculating.
The amount of cookies baked was 28 cookies
Solution for how many cookies your mother bake altogetherlet the number of pumpkin cookies be x
half of them on a plate for your brother and you
= x - x/2 = x/2
Your dog Gobbles ate six
= x/2 - 6
Your brother ate half of what was left
= (x/2 - 6)) / 2
= x/4 - 3
you ate the last four means that what was left is equal to 4
x/4 - 3 = 4
x - 12 = 16
x = 16 + 12
x = 28
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which of the following fractions is smaller 4/9 or 1/5
Answer:
1/5
Step-by-step explanation:
these fractions are proper fractions
Answer: 1/
Step-by-step explanation:
You have $18 and earn $0.25 for each cup of orange juice you sell. Write an equation that represents the total amount A (in dollars) you have after selling j cups of orange juice.
Answer:
A = 0.25*j + 1
Step-by-step explanation:
Answer:
[tex]A = 18 + \frac{j}{4}[/tex]
Step-by-step explanation:
A = 18 + j/4
A = Amount in $
Starting amount is 18 and a 1/4 dollar is earned for every cup of juice sold.
If a gallon of paint costs $18 and covers 180 ft²,
how much does it cost to paint a 900 ft² wall
Answer:
$90
Step-by-step explanation:
180x5 equal 00
$18x5 equals $90
i really need help. Strawberries cost $2.13 per pound and Annie purchased 1.2 pounds. How much did she pay for strawberries if her answer is rounded to the nearest cent?
Annie paid a total of $2.6 for 1.2 pounds of strawberries
How to determine the amount paid?In this question, we have the following parameters:
Unit cost per pound = $2.13 per pound
Number of pounds = 1.2 pounds
The amount paid for the number of pounds is represented by the equation
Amount paid = Unit cost per pound x Number of pounds
Substitute the known values in the above equation So, we have the following equation
Amount paid = 2.13 * 1.2
Evaluate the products
Amount paid = 2.556
Approximate
Amount paid = 2.6
Hence, the amount is $2.6
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Answer:
2.56
Step-by-step explanation:
the united nations stores data about the kilowatt-hours of wind power produced around the world. the following data set gives information of the united states for 25 years, from 1990 to 2014, in units of million kilowatt-hours. using a calculator or statistical software, find the linear equation of the first 11 years of data, from 1990 to 2000. round the slope to two decimal places and the y-intercept to the nearest whole number. provide your answer below:
The value that the linear equation predicts for the year 2001 is 4652.15
The discrepancy between the actual and anticipated value is 2173.85
Given data;
Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.
The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.
To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.
It will be written as y = m(x) + c.
where,
The dependent variable is y. (in our example is quantity)
The independent variable is x. (in our example is the year)
'm' is equal to the slope of the variable X.
'C' is a constant.
The fitted equation is provided as follows:
Quantity = 186.87 (year) - 369274.72
Now that the value for the year 2001 has been provided,
Quantity = -1868.87 -369274.72
Quantity = 4652.15
The value that the linear equation predicts for the year 2001 is 4652.15.
The precise figure for 2001 is 6806.
For the year 2001, the discrepancy between the actual and anticipated values is
6806 - 4652.15 = 2173.85
The distinction is 2173.85.
(2173.85/6806)*100 is the percentage difference.
As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.
Hence,
The value that the linear equation predicts for the year 2001 is 4652.15
The discrepancy between the actual and anticipated value is 2173.85
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What is the answer to 4r - 9r - 11r + 7r
Answer:
-11r
Step-by-step explanation:
4r - 9r = -5r
-5r - 11r = -16r
-16r + 7r = -11r