The two numbers with the sum of 5 are 0 and 5
How to determine the two numbers?The sum of the numbers is given as
Sum = 5
The relationship between the numbers is given as
Three times the first is thirteen more than ten times the second.
This can be rewritten as
3x = 15 + 10y
Where x and y represent the numbers
This means that
x + y = 5
Make x the subject
x = 5 - y
Substitute x = 5 - y in 3x = 15 + 10y
3(5 - y) = 15 + 10y
Expand
15 - 3y = 15 + 10y
Evaluate the like terms
13y = 0
This gives
y = 0
Substitute y = 0 in x =5 - y
x = 5 - 0
Evaluate
x = 5
Hence, the numbers are 0 and 5
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Can anyone help me with this?
The line shown in the graph have slope of line as 13/27 with rise 13 and run 27.
What is slope of line?
The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in comparison to other lines shown on the same coordinate plane.
The formula to calculate the slope of any line is given by:
[tex]slope = \frac{rise}{run}[/tex]
We know that, '
rise = y₂ - y₁
run = x₂ - x₁
As we can see in the graph
x₂ = 10, y₂ = 3
x₁ = -7, y₁ = -10
putting the values in above formula
rise = y₂ - y₁ = 3 -(-10) = 13
run = x₂ - x₁ = 10 -(17) = 27
so, slope = 13/27
Hence the slope of the line shown in graph is 13/27.
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For the function g, g(3)= -11 and g(7)= 5. What is the function rule for g(x)?
Answer:
g(x) = 4x - 23
Step-by-step explanation:
We will assume a linear function for g(x)
This will be of the form g(x) = ax + b where a and b are constants
Given the info,
g(3) = a(3) + b = -11
g(7) = a(7) + b = 5
Thus we have two equations in a and b
3a + b = -11 [1]
7a + b = 5 [2]
Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11
4a = 16
a = 4
Substitute for a in equation [2]:
4(7) + b = 5
28 + b = 5
b = 5-28 = -23
So equation of g(x) is
g(x) = 4x - 23
What is r, -3(1+6r)=14-r
Step-by-step explanation:
-3(1+6r) = -3-18r =14-r
17r = -17 Therefore, r = -1
factor the GCF from 16p^4+4p^3
Given the expression:
[tex]16p^4+4p^3[/tex]The GCF of p^4 and p^3 = p^3
And the greatest common factor of 16 and 4 = 4
so,
[tex]\begin{gathered} \frac{16p^4}{4p^3}=4p \\ \\ \frac{4p^3}{4p^3}=1 \end{gathered}[/tex]So, the factors of the given expression will be:
[tex]16p^4+4p^3=4p^3(4p+1)[/tex]2/3x+2y=12 in standard form
Answer:
[tex]2x + 6y = 36[/tex]
[tex]x + 3y = 18[/tex]
Rational Expressions
a) The area of a rectangle is x - (16/x). The width is (x/4) + 1. Find an expression to represent the length
b) The volume of a rectangular prism is (7/x) - (3/5x). The width is 2/x and the hight is 4/x, what is the length?
(a) The expression to represent the length of the rectangle is
h = (x-16/x)/(x/4+1).
(b) The length of the rectangular prism is L = ((7/x)-(3/5x))/(2/x)(4/x).
What is a rectangle?A rectangle is a quadrilateral with all four interior angles measures of 90°.
(a) Given that, the area of the rectangle is x-16/x and its width is x/4 +1.
Let the length of the rectangle be h, then it follows:
h×(x/4 + 1) = x - 16/x
h = (x-16/x)/(x/4+1)
Hence, the expression to represent the length of the rectangle is
h = (x-16/x)/(x/4+1).
(b) Given that, the volume of the rectangular prism is (7/x)-(3/5x), the width is 2/x, and the height is 4/x.
Let the length of the rectangular prism be L, then it follows:
L× (2/x) ×(4/x) = (7/x)-(3/5x)
L = ((7/x)-(3/5x))/(2/x)(4/x)
Hence, the length of the rectangular prism is L = ((7/x)-(3/5x))/(2/x)(4/x).
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Write an equation of the line that passes through the given point and has the given slope. (−5, 4); slope −3
Answer:
y = -3x - 11
Step-by-step explanation:
Slope = -3
so...
-3x
y = -3x + (b)
given : (-5, 4) x=-5 y=4
4 = -3(-5) + b
4 = 15 + b
b = -11
so...
y = -3x - 11
The table of values below shows the amount of water in a watering can and the weight of the can. Based on this information, how much does a gallon of water weigh?
Amount of Water in Can (gallons) Weight of Cans (pounds)
0 2
0.5 6.2
1 10.4
1.5 14.6
2 18.8
A
4.2 pounds
B
6.2 pounds
C
8.4 pounds
D
10.4 pounds
Each gallon of water weighs by itself is 8.4 pounds, option (C) 8.4 pounds is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
From the data given:
When the Amount of Water in Can (gallons) = 0
Weight of Cans (pounds) = 2
It means the weight of the can = 2 pounds
For the 0.5 gallons, the weight of the can = 6.2 pounds
For the 0.5 gallons, the weight of the water = 6.2 - 2 = 4.2 pounds
For the 1 gallon, the weight of the water = 2x4.2 pounds
= 8.4 pounds
Thus, each gallon of water weighs by itself is 8.4 pounds, option (C) 8.4 pounds is correct.
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the equation y=12.7x+15.2 estimates the amount that businesses will spend, in billions of dollars, on internet software to conduct transactions via the web, where x is the number of years after 2002. for what years will the spending be more than $66 billion?
The years when the spending be more than $66 billion is in 4 years time.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The equation is given as y=12.7x+15.2 and the amount is $66 billion. Therefore, the value of x will be:
y=12.7x+15.2
66 = 12.7x + 15.2
Collect like terms
12.7x = 66 - 15.2
12.7x = 50.8
Divide
x = 50.8 / 12.7
x = 4
The number of years is 4.
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In AJKL, j = 74 cm, k = 14 cm and l=80 cm. Find the measure of ZJ to the nearestdegree.
To answer this question we first draw the triangle to help us:
As a note on the problem: This is not necessarily the triangle we have, we drew just to helps us solve it.
Now, to find the angle J we can use the law of cosines:
[tex]j^2=k^2+l^2-2kl\cos J[/tex]Plugging the values we have and solving for J we have:
[tex]\begin{gathered} 74^2=14^2+80^2-2(14)(80)\cos J \\ 2(14)(80)\cos J=14^2+80^2-74^2 \\ \cos J=\frac{14^2+80^2-74^2}{2(14)(80)} \\ J=\cos ^{-1}(\frac{14^2+80^2-74^2}{2(14)(80)}) \\ J=60 \end{gathered}[/tex]Therefore the angle J is 60°.
Find the volume of the cylinder
Answer: 150.72 in^3
Step-by-step explanation:
the radius (r) is 2 because the diameter of the cylinder is 4.
the height (h) is 12 (obviously because that's provided in the picture.)
the formula to find the volume of the cylinder is:
[tex]3.14(2^2)\times 12[/tex]
therefore, it is 150.72 in^3
i hope this helps :)
The diagram shows a simple bridge, which is supported by four steel cables.
A. Find the angles at A and B
B. Find the length of each cable
(a)
In the given diagram,
∠α and ∠β can be determined using trigonometric functions,
tan α = Opposite side/Adjacent side
⇒ tan α = 4/6
⇒ tan α = 2/3
⇒ α = tan^-1 (2/3)
⇒ α = 33.7°
Similarly,
tan (α + β) = 4+4/6
⇒ tan (α + β) = 8/6
⇒ tan (α + β) = 4/3
⇒ (α + β) = tan^-1 (4/3) = 53.1°
⇒ 33.7 + β = 53.1°
⇒ β = 19.4°
(b)
For the cables adjacent to the perpendicular height, i.e., adjacent to ∠α, on both the sides
Cable length^2 = 4^2 + 6^2 .............................. (Pythagoras theorem)
⇒ Cable length^2 = 16 + 36
⇒ Cable length^2 = 52
⇒ Cable length = 7.21 m
For the cables far from the perpendicular, on both the sides,
Cable length^2 = 6^2 + 8^2 .............................. (Pythagoras theorem)
⇒ Cable length^2 = 36 + 64
⇒ Cable length^2 = 100
⇒ Cable length = 10 m
What is Trigonometric Function?The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. The main division of trigonometric functions is into sine, cosine, and tangent angles. Additionally, the three fundamental functions can be used to derive the cotangent, secant, and cosecant functions. Basically, compared to the fundamental trigonometric functions, the other three functions are frequently used. The lengths of the adjacent and opposing sides are compared to determine the tangent function.
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In triangle ABC, the measure of b is three times larger than the measure of C. The measure of A is twice as large as the measure of C. The sum of the angles in a triangle is 180°.
The value of angle a, b and c in the triangle are 60, 90 and 30 degrees respectively and the summation of these angles is equal to 180 degree.
Sum of Angles in TriangleThe total sum of angles in a triangle is equal to 180 degrees.
To solve this problem, we have to write out equations to represent the unknown values.
Let;
a = xb = yc = zMathematically,
[tex]a + b + c = 180^0[/tex]
Let's represent each of the statement mathematically;
[tex]y = 3z...eq(i)\\x = 2z ...eq(ii)\\[/tex]
Let's substitute the values and find the value of angle C
[tex]a + b + c = 180\\2z + 3z + z = 180\\6z = 180\\z = 30\\c = 30^0\\b = 90^0\\a = 60^0[/tex]
From the calculations above, the value of a, b and c are 60 degrees, 90 degrees and 30 degrees respectively.
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consider this equation
(4x) 1/3 - x =0
the first step to solving this equation is to
A. take the cube root of both sides
B. cube both sides
C. add x to both sides
the second step is to
A. add the cube of x to both sides
B. add the cube root of x to both sides
C. cube both sides
solving this equation for x initially yields
A. one possible value
B. three possible values
C. two possible values
checking the solutions shows that
A. 0 and 2 are valid solutions
B. only 0 is a valid solution
C. -2,0, and 2 are valid solutions
D. none are valid solutions
The first step to solving the equation is to; C. add x to both sides
The second step to solving the equation is to; C. cube both sides
Solving the equation for x initially yields; C. two possible values
Checking the solutions shows that; D. none are valid solutions
How to solve Linear Equations?We are given the linear equation;
4x[tex]^{1/3}[/tex] - x = 0
From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;
4x[tex]^{1/3}[/tex] - x + x = 0 + x
4x[tex]^{1/3}[/tex] = x
Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;
(4x[tex]^{1/3}[/tex])³ = x³
4³x = x³
64x = x³
Divide both sides by x to get;
x² = 64
Take square root of both sides to get;
x = ±√64
x = ±8
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HOW DO I GET 36.9 OUT OF THE NUMBERS 55.5 AND 35
Answer:
Add 55.5 and 35, then subtract 36.9.
Step-by-step explanation:
x+36.9=55.5+35
x+36.9=90.5
Subtraction Equality
x + 36.9 + (-36.9)= 90.5 (-36.9)
x = 53.6
Solving Systems of Equations by Substitution
-2x-y=-9
5x-2y=18
explain please.
Answer:
(4,1)Step-by-step explanation:
Systems of equations may be solved in one of two manners: substitution and graphing. This requaests they be solved by substitution, but I'll add the graphing solution, also.
Substitution:
We want to eliminate one of the two variables to result in an expression that only has one of the two remaining. We can do that by manipluating one of the equations such that, when it is combined with the other, results in the elimination of one of the variables.
Given:
-2x-y=-9
5x-2y=18
we can multiply or divide one of the equations so that one of the terms has equal, but opposite, values. We could multiply the first equation by 2.5 so that it becomes -5x -2.5y = 9*(2.5). Then it could be added to the second to eliminate the x term.
My preference is to find a way to avoid fracticious fractions, so I will multiply the first equation by -2 so that we can eliminate y:
-2*(-2x-y =-9)
4x+2y = 18
No add this to the second equation:
4x+2y = 18
5x-2y = 18
9x = 36
x = 4
Since x = 4:
-2x-y=-9
-2*(4)-y=-9
-8 - y = -9
y = 1
The solution is (4,1). It is the point the satisfies both equations.
-2x-y=-9
-2(4)-(1)=-9
-8-1=-9 YES
----
5x-2y=18
5(4)-2(1)=18
20 - 2 = 18 YES
Graphing:
The solution to these equations is the point at which the lines intersect. See the attached graph. The lines intersect at (4,1).
Can someone solve this and explain the process
Sin 73° has a value of 0.9563. (approximately).
Define trigonometric ratios.Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle. If you know the lengths of two of the triangle's sides, you can use trigonometric ratios to get the measurements of one (or both) of the acute angles.
Given Data
Trigonometric ratio of
sin73°
The sine trigonometric function for an angle of 73 degrees has a value of sin 73 degrees.
Sin 73° has a value of 0.9563. (approximately).
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A mixture of juices in a punch had 1.1 L of pineapple juice for every 0.4 L of orange juice. Sarah wanted the punch to taste more orangey, so she added 0.3 L of orange juice but no pineapple juice. Now the ratio of juices was 1.1 L of pineapple juice for every 0.5 L of orange juice. How many litres of punch did Sarah have now
Answer:
1.1l +0.4+0.3+0.5
answer = 2litres 3milimetres
Simplify as far as possible without a calculator.
(
3
−
√
7
)
(
3
−
√
7
)
Answer:
- 26
Step-by-step explanation:
(3−√7)(3−√7)
9 - 3√7 -3√7 + √7√7
9 - 6√49 + √49
9 - 6*7 + 7
9 - 42 + 7
= -26
Evaluate each of the following given that f(x) =2x+10, find:f(-3)
Answer:
4
Step-by-step explanation
find the equation of ab and bc in the following square
In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
The formula for a2 + b2 + c2 is written as a square plus b square plus c square. A2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca) is how it is expanded.
Give an example to explain what square is?
A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. Many objects can be found in your surroundings that have a square shape.
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3/10 +1/4 + 4/5 =
answer in the simplest form
3/10 +1/4 + 4/5 = 27/20
5 girls decide to only spend $40 between them. on average, how much money can each girl spend? Write an inequality. Each sister has 10 dollars
40 = 5X
X = 10 dollars
Now divide 40/5 = 8
On average, each girl spends $8 dollars
Now write an inequality ,for this situation
5X ≤ 40
(a + b + c + d + e)/5 = 40
jeffrey has $1.20 more than ryan. when ryan hands jeffrey $7.50, jeffrey's money becomes 7 times as much as Ryan's. How much money did they each have at the beginning?
Answer:
Ryan had 10.20 dollars and Jeffery had 11.40 dollars.
Step-by-step explanation:
Let Ryan have x dollars originally, then Jeffrey has x + 1.20 dollars.
From the given info:
After getting 7.50 from Ryan, Jeffrey has:
x + 1.2 + 7.5 dollars and Ryan has x - 7.50 dollars.
Jeffreys money is now is 7 times as much as Ryan's, so:
x + 8.7 = 7(x - 7.5)
x + 8.7 = 7x - 52.5
8.7 + 52.5 = 7x - x
6x = 61.2
x = 10.20 dollars.
Given f(x) = -4x - 2, find f(1).
Answer:
-6
Step-by-step explanation:
Replace the variable x with 1 in the expression.
f(1)=−4−2
Then simplify -4 and -2 (subtract 2 from -4)
= -6
3. Un objeto se mueve a una velocidad de
23 m/s. Acelera a una velocidad de 85
m/s en un tiempo de 8.3 s. ¿Qué
aceleración experimenta?
The most appropriate choice for acceleration will be given by
Acceleration of the body = 7.59 [tex]m/s^2[/tex]
What is acceleration of a body?
At first it is important to know about velocity of a body.
The rate of change of displacement of a body is called velocity of a body. Velocity is a vector quantity.
The rate of change of velocity of a body is called acceleration.
Acceleration is also a vector quantity as the direction is taken into account
Here,
Initial velocity of an object = 23m /s
Final velocity of an object = 85 m/s
Time = 8.3 s
Acceleration of the object =
[tex]\frac{85 - 23}{8.3}\\\\\frac{63}{8.3}\\\\[/tex]
7.59 [tex]m/s^2[/tex]
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Please help me on this question I need full explanation
Answer: parrallelograms have 4 sides
Step-by-step explanation:
If 672,342= 6.72342x 10n what is the value of n
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of n in the equation 672,342 = 6.72342 x 10n is 10,000
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 9 is an equation.
6x+ 2 = 9 is ana equation.
We have,
672,342 = 6.72342 x 10n
Divide both sides by 6.72342
672,342 / 6.72342 = 10n
We get,
100000 = 10n
Divide both sides by 10.
100000 / 10 = n
n = 10,000
Thus,
The value of n in the equation 672,342 = 6.72342 x 10n is 10,000
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What table represents a function?
Table A represents a function.
Define functions.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Functions are crucial instruments in the creation of mathematical models because we continually develop beliefs about connections between variables in nature and society. Typically, functions in school mathematics contain numerical inputs and outputs and are frequently specified by algebraic expressions.
Given,
Table A represents a function,
A visual table with columns and rows that shows the function in relation to the input and output is called a function table. Function tables are frequently referred to as function machines by younger students. Each function has a rule that governs how the input and output are related to one another.
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what is the probability of rolling at least one even number or a sum of 3 using two number cubes?
Answer:you could do
You would need to rile a two and a one together though
