Answer:
it should be the first one, if not it’s the third
Step-by-step explanation:
Read Zalika's number problem.
' I am thinking of a number N. Twice (N+10) is the same as four times (N-10) '
a. Write down an equation to show this.
b. Solve the equation to find the vale of N.
Part A
The equation that shows the statement is
2N + 20 = 4N - 40
Part B
The value of N = 30
The number that he is thinking = N
Twice (N+10) = 2(N+10)
= 2N + 20
Four times (N-10) = 4(N - 10)
= 4N - 40
Twice (N+10) is the same as four times (N-10)
The equation that represent the given statement is
2N + 20 = 4N - 40
Part B
Solve the equation
2N + 20 = 4N - 40
4N - 2N = 20 + 40
2N = 60
N = 60/2
Divide the terms
N =30
Hence,
Part A
The equation that shows the statement is
2N + 20 = 4N - 40
Part B
The value of N = 30
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Find the length of the missing segment.
In accordance to Thales's theorem, the geometric system has a missing side length of 15 units.
How to determine missing lengths in geometric systems by ratiosIn this problem we find a geometric system formed by two proportional trapezoids. This similarity and proportionality is defined by Thales's theorem, which states that a triangle segmented by several lines parallel to each other and parallel to the base of the figure creates triangles and quadrilaterals proportional to each other.
Then, two figures of the given trapezoids are represented by side proportionality ratios. Then, the proportionality ratio is described and its variable x is cleared within by algebra properties:
First, define the proportionality ratio associated to the geometric system:
4 / (10 + 4) = (21 - x) / 21
Second, simplify the equation and clear the variable x:
4 / 14 = 1 - x / 21
2 / 7 = 1 - x / 21
42 / 7 = 21 - x
6 = 21 - x
x = 21 - 6
x = 15
The missing length is equal to 15 units.
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simplify 8^15 ÷8^-3 math is hard for me
Answer:
8^18
Step-by-step explanation:
8^15
8^−3
=
8^15
8−3
= 8^15− (−3)
= 8^18
Gabriella is going back to school shopping.each notebook she buys costs $3 and each pack of markers costs $3.she buys 4 packs of markers and n notebooks.she writes the follwing expression represent how much shr spend
Answer:
$24
Step-by-step explanation:
3(4) + 3(4) = x (the total cost)
12 + 12 = x
x = $24
marrisa bought 3 packages of balloons and 4 packages of party favors for a total of 14.63. Ray bought 2 packs of balloons and 4 packs of party favors for a total of 16.03. find the price of a pack of balloons and the price of a pack of party favors
The price of a pack of balloons is 4. 39
The price of a pack of party favors is 0. 36
How to determine the valuesWe have that;
Let the cost of balloons be x
Let the cost of party favors by y
From the information given, we have that;
3x + 4y = 14. 63 (1)
2x + 4y = 16. 03 (2)
Now, let's make 'x' the subject from equation (1)
x = 14. 63 - 4y/ 3 (3)
Substitute in equation (2)
3( 14. 63 - 4y/ 3) = 16. 03
expand the bracket
43. 69 - 12y /3 = 16. 03
cross multiply
43. 69 - 12y = 48. 09
collect like terms
- 12y = - 4. 4
make 'y' the subject
y = 0. 36
substitute in equation (3)
x = 14. 63 - 4(0. 36)/ 3
x = 13. 1/ 3
x = 4. 39
Hence, the prices are 4. 39 and 0. 36 respectively.
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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{1}{6}[/tex] x + 9
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (6, 10) ← 2 points on the line
m = [tex]\frac{10-9}{6-0}[/tex] = [tex]\frac{1}{6}[/tex]
the line crosses the y- axis at (0, 9 ) ⇒ c = 9
y = [tex]\frac{1}{6}[/tex] x + 9 ← equation of line
Solve. −1 − 10x < −1
The solution to the inequality is x > 0
What is Inequality?Inequality in mathematics differentiate two values, if one is less than, greater than, or not equal to another value
Evaluate the equation by letting the unknow to be on one side
−1 − 10x < −1
-10x < -1+1
Add +1 to both sides
= -1-10x+1 < -1+1
= -10x < 0
Divide both sides by -10 same factor and flip the relation because of negative factor
= -10x /-10 > 0/-10
= x > 0
Therefore the solution to the inequality is x>0
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You multiply two integers and the product is -18. List 4 possible pairs of integers
The possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)
We need to find the four possible pairs of integers that has product -18
Let x and y be two required integers.
Since the product is negative, one of the integer must be negative integer.
x y x*y
9 -2 -18
2 -9 -18
18 -1 -18
-1 18 -18
6 -3 -18
3 -6 -18
Therefore, the possible pairs of integers that has product -18 is: (9, -2), (18, -1), (6, -3), (3, -6), (2, -9)
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Help Please!!!
Direct and Inverse Variations
aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given sequence is 5,9,13,17,21
Five comma nine comma thirteen comma seventeen comma twenty one.
We need to find the nth term of the sequence.
Firstly we need to find the sequence is AP or GP.
An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.
so 9-5=4,
13-9=4
Hence the sequence is a Aritmetic sequence.
In arithmetic sequence the nth term can be find by using the formula
aₙ=a+(n-1)d
where a is first term and d is common difference.
Hence aₙ=a+(n-1)d is the formula can be used to find the nth term of the sequence.
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400 kilometers in 8 hours at a constant speed
Solve the inequality 2m - 125 or 5m> -25.
Answer:
m = -5
Step-by-step explanation:
I'm not sure of the first part, but this is how to solve the second:
5m > -25
5m/5 > -25/5
m = -5
State the value of the two square numbers closest to 55. Hence, show that 55 is not a square number.
Answer:
7.416 is the answer
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, -6) and (-8, 2)
The distance between the two points is 8.25 units
What is meant by the distance between two points?The distance between two points in a plane is the length of the line segment separating the two locations. Typically, the equation d=((x2 - x1)2 + (y2 - y1)2) is used to calculate the distance between two locations. You may use this formula to get the separation between any two points on an x-y plane or coordinate plane.
The following is the formula for the separation between two points:
d= √(x₁-x₂)²+(y₁-y₂)²
Points (x1, Y1) and (x2, Y2)
As given in the question, the points are (-6, -6) and (-8, 2)
The distance between the two points is,
d= √(-6+8)²+(-6-2)²
d=√4+64
d=√68 units= 8.25 units
Therefore, the distance between the two points is 8.25 units
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What is an
equation of the line that passes through the points (6, 0) and (3, 4)?
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
What are the different forms of straight lines ?
The following information about the straight line is required if we wish to obtain the equation for it.
1. The y-intercept and slope
2. Two-point and slope
3. Two things.
4. the intersection of the x- and y-axes
the straight line that passes through (6,0) and (3,4).
The equation can be expressed in a point-slope form which is ,
y/x-6=4/-3
∵ -3y=4(x-6)
Hence,
The equation that passes (6,0) and (3,4) is -3y=4(x-6)
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The local craft fair charges the vendors a flat rate of $15 plus $10 for each hour that they splend at the fair. If the vendor owed $65, how many hours did he remain at the craft fair?
Answer:
5 hours
Step-by-step explanation:
$65 - $15 = $50
$50/$10 = 5
Expand and simplify (2x + 5)2
Answer: 4x+10
simplified: 2x+5
Step-by-step explanation:
Answer: 4x+10
You multiply 2 by (2x) = 4x
You multiply 2 by (5) = 10
I need help asap please now please !!!!!!!!!!!
Here is a correlation, does it also represent causation? Explain you answer.
The number of cold, snow days and the amount of hot chocolate sold at a ski resort.
Between the two variables, the number of cold, snow days, and the amount of hot chocolate sold at a ski resort, there is causation.
Is causation in this relation?For two variables x and y, we have causation when a change in one of the variables causes an immediate change in the other variable as a response.
Here we have the two variables:
x = number of cold, snow days.
y = amount of hot chocolate sold at a ski resort.
Obviously, there is a correlation there, we can even assume that if the days are cold enough, a larger percentage of the people in the ski resort will decide to stay there, and then there is a larger posibility that they will consume hot chocolate there, so yes, there is causation between these two variables.
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The dimensions of a rectangle can be expressed as x+4 and x-3. If the area of the rectangle is 60 inches squared, find the dimensions of the rectangle
Step-by-step explanation:
length(l)=x+4
breadth(b)=x-3
Area of rectangle(A)=l×b
60=(x+4)×(x-3)
60=x^2-3x+4x-12
60=x^2+x-12
x^2+x-12-60=0
x^2+x-72=0
x^2+9x-8x-72=0
x(x+9)-8(x+9)=0
(x+9)(x-8)=0
equating equation
x+9=0.....eq(i)
x=-9 it is not possible
x-8=0.....eq(ii)
x=8
Then,length(l)=x+4
=8+4=12
breadth(b)=x-3
=8-3=5
please help me with this
Answer: final answer = 3/8
Step-by-step explanation:
it says 1/8 + 1/4. before you can add them you have to make sure that both fractions have the same denominator first you have to make both of the bottom denominators the same so its 1/8+2/8.
1/8+2/8=3/8
- is slightly variable - and follows a nearly normal distribution - with a mean of 25 square feet - and a standard deviation of 3 square feet. (a) what is the probability that - the area covered by a can of spray paint - is more than 27 square feet?
The probability that the area covered by a can of spray paint is 0.251
The variable of interest is:
X: are objects that can be painted with a single can of spray paint.
This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.
Symbolically:
P(X≥27)
To calculate the probability, use the standard normal distribution, so first standardize the value of X using:
Z= (X-μ)/σ
P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)
Now, because the Z-table contains cumulative probability information:
P(Zα≤Z₀)=1-α
you must perform the following conversion to calculate the requested probability:
1 - P(Z<0.67)= 1 - 0.749= 0.251
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what are the coefficients in 4x + 8y - 5
Answer:
Step-by-step explanation:
A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.
The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).
you are going to paint the 6-sector spinner shown. there are 4 colors to choose from. 0 how many different ways can you paint the spinner, if each color can be used more than once, and: there are no other restrictions?
The different ways can paint the spinner is [tex]4^{6}[/tex].
Permutation and Combination:
A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
Here it is given that to paint the 6-sector spinner shown there are 4 colors to choose from.
The total number of ways to color this spinner with 6 different parts and 4 different colors is 4 × 4 × 4 × 4 × 4×4 = [tex]4^{6}[/tex] ways
Therefore the ways is [tex]4^{6}[/tex].
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Need help asap
Solve by using elimination. Express your answer as an ordered pair.
3x−2y=11
3x−y=7
The solution to the given set of systems of equations is (x, y) = (1, -4).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let's determine the solution using the elimination Method
3x−2y=11 (Equation 1)
3x−y=7(Equation 2)
Multiply the second equation by 2.
6x - 2y = 14 (Equation 3)
Now subtract the first equation from third to eliminate the y.
6x - 2y - (3x - 2y) = 14 - 11
3x = 3
x = 1
Now to find the value of y,
3x−y=7
3(1) − y = 7
y = 7 - 3
y = -4
Therefore, the solution to the given set of systems of equations is (x, y) = (1, -4).
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Write an equivalent ratio for each ratio
Answer:2/5=4/10 and 1/4=2/8
Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
–72, –71, –70, –69, ..
Answer:
-73 +n
the first term is -73+1
the secound is -73+2
and so on
Answer:
[tex]a_{n}[/tex]= n - 73
Step-by-step explanation:
there is a common difference between consecutive terms , that is
- 71 - (- 72) = - 70 - (- 71) = - 69 - (- 70) = 1
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 72 and d = 1 , then
[tex]a_{n}[/tex] = - 72 + 1(n - 1) = - 72 + n - 1 = n - 73
Write a system of equations with the solution (4, -3).
The system of equations with the solution (4, -3) is y = x - 7 and y = 2x - 11.
We are given a point. The coordinates of the point are (4, -3). We need to find a system of equations such that they pass through the given point.
We will use the slope-point form of a line. Let the slope of the equation of the straight line be "m". We need two equations. The general equation of a line using the slope-point form is given below.
(y - y1) = m(x - x1)
We know that both equations must pass through the given point for the solution to exist.
(y - (-3)) = m(x - 4)
(y + 3) = m(x - 4)
We just need to take any two values of the slope of the line.
First, we take m = 1. The corresponding equation is given below.
(y + 3) = m(x - 4)
(y + 3) = 1*(x - 4)
y + 3 = x - 4
y = x - 7
Next, we take m = 2. The corresponding equation is given below.
(y + 3) = m(x - 4)
(y + 3) = 2*(x - 4)
y + 3 = 2x - 8
y = 2x - 11
Hence, the system of equations is y = x - 7 and y = 2x - 11.
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What is the name of the bolded part of this shape?
Answer:
A right-angled triangle
Drag the red and blue dots along the x-axis and y-
Answer:
Put one dot at (0,3) and the other dot at (1,0)
Step-by-step explanation:
Let x = 0
6x + 2y = 6
6(0) + 2y = 6
2y = 6 Divide both sides by 2
y = 3
(0,3)
Let y = 0
6x + 2y = 6
6x + 2(0) = 6
6x = 6 Divide both sides by 6
x = 1
(1, 0)
you need to construct a fence around an area of 1600ft2 . what are the dimensions of the rectangular pen to minimize the amount of material needed?
The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.
What is the meaning of minimum dimension?The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.
With regard to the above problem,
let us say L is the lenght of the rectangle and W is the width
Based on the formula for the area of a rectangle,
L x W = 1600ft
To minimize the perimeter, of the rectangle, we must assume that:
L = W
that is L² = 1600
If we applied square root to both sides of the equation, we'd have
L = 40
Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.
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