We can solve the given linear equation 7x = 5y by plotting the graph of x and y on the coordinate plane.
An equation is known to be a linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b and c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
First, solve for x
7x = 5y
Divide both sides by 7
7/7 x = 5/7 y
Dividing by 7 undergoes the multiplication by 7
x = 5/7 y
Similarly, solve for y
7x = 5y
Divide both sides by 5
7/5 x = 5/5 y
Dividing by 5 undergoes the multiplication by 5
y = 7/5 x
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How can you tell if a linear system has infinitely many solutions?
A linear system has infinite solutions if it consists of exactly the same equations.
The 3 possible solutions of a linear system are:
- Unique or one solution
- Infinite solutions
- No solution
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
Example:
3x + 2y = -4 ..... (equation 1)
6x = -4y - 8 ..... (equation 2)
Add 4y to both sides of equation 2:
6x + 4y = -8
Divide both sides by 3:
3x + 2y = -4
Hence, equation 2 is exactly the same as equation 1. If we plot their graphs, they will share the same graph. Any solution of equation 1 is also solution of equation 2. Therefore, this linear system has infinite solutions.
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What is the smallest positive multiple of $13$ that is greater than $500?$
Answer:
Step-by-step explanation:
The smallest possible multiple of 13 dollars greater than 500 dollars would be 507 which is 13*39 (i assume you mean whole numbers when you say positive numbers, if not the other answer would be 13*38.461)
Sam recorded the effects of exercise on short-term memory. Which of these is a response variable ?
A. Exercise
B. Neither exercise nor short-term memory
C. Short term memory
D. Both exercise and short-term memory
Short term memory is a response variable as it is dependent. Hence Option C is the answer.
What is response variable?A dependent variable is the response variable. It is reliant on the independent variable, which serves as the explanatory variable.
What is the predicting factor?Explanations for the findings revealed by the response variables are provided by the explanatory or independent variables. Explanatory response is qualitative since it is classified based on a category.
The response variable is what the researcher often measures in research studies. The response variable in the example presented above is short-term memory, which is influenced by exercise.
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Does a quadratic graph have an inverse?
The inverse of a quadratic graph is a square root function. To graph the inverse, we reverse the domain and range.
What is a quadratic graph?The curve-shaped graph of a quadratic function is known as a parabola. The vertex of a parabola is one of its focal points.
On the graph, it is either the highest or lowest point.
We can imagine it as the parabola's endpoint.
A square root function is the inverse of a quadratic function.
We switch the domain and range in order to graph the inverse.
The graph has the same structure but has been rotated to have the original function's domain and range switched.
Therefore, the inverse of a quadratic function is a square root function. To graph the inverse, we reverse the domain and range.
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For what value of k do the pair of linear equations KX − 4y 3 and 6x − 12y 9 have an infinite number of solutions?
The pair of linear equations KX − 4y = 3 and 6x − 12y = 9 have an infinite number of solutions when K = 0.
This can be shown by solving the two equations for K. Solving the first equation for K yields K = (4y/X) + 3. Substituting this into the second equation yields: 0 = (4y/X) + 3 - (12y/6x). Simplifying this yields 0 = (2y/X) - (9/6x). This equation simplifies to 0 = (2y - 9x)/X. Since the denominator of the right side of the equation is not equal to 0, the only way to get 0 = 0 is if the numerator is equal to 0 as well. This happens when 2y - 9x = 0. Since y and x are variables, the only way that this equation can be true for all values of x and y is if the coefficient of both of them is equal to 0. Thus, K = 0 is the only value for which this pair of linear equations has an infinite number of solutions.
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What equation represents this sentence?
5 less than a number is 12.
5=n-12
n-5=12
5-n=12
5=12-n
ill give brainliest its due at 11:59 its 8pm
Answer:
I'm sure its 5=n-12 :))))
Imagine you have a wood block that is 4 cm wide, 4 cm long, and 8 cm high. It
weights 200 grams.
What is the volume of the block? Be sure to include the units.
Then, imagine that you are cutting the block into 2 exactly equal halves. What is the
volume of one of the pieces (including the units)? How does its volume compare to
that of the original block?
The way that the new volume compares to the original volume of the block is that the new volume is half of the original volume.
How to find the volume of the block?The volume of a rectangular block is gotten from the formula;
Volume = length * width * height
Now, we are given;
Width = 4 cm
Length = 4 cm
Height = 8 cm
Thus;
Volume of block = 4 * 4 * 8
= 128 cm³
Now, if you are cutting the block into 2 exactly equal halves, then you can say that;
New length = 4/2 = 2cm
Thus;
Volume of cut block = 2 * 4 * 8
= 64 cm²
This is concluded to be half of the original block.
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ORIGINAL ANSWERS PLEASE
A student's course grade is related to class attendance. The grade can be modeled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. For a student who was in attendance for 75 days and has a grade of 82%, find and interpret the residual.
The residual of the given situation is 0.8
What is residual of a function?The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.
Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,
Finding the actual value,
y = 0.66 × 75 + 33.3
y = 82.8
The predicted value = 82
Residual = actual y value − predicted y value
Therefore,
Residual = 82.8-82 = 0.8
Therefore, y = 0.8
Hence, the residual of the given situation is 0.8
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Find m angle Bm∠Bm, angle, B.
Note that m angle Bm∠Bm, angle, B is acute. Round to the nearest degree
The measure of angle B where angle B is an acute angle by using the Law Of Sines is 61° .
What is an Acute Angle ?
The Acute Angle can be defined as an angles that measure less than 90° , the acute angle is smaller than Right Angle and also smaller than the Linear Angle ( measuring 180° ).
From the figure ,
we can see that the measure of the sides are given as a = 9 , b = 8 and
the measure of angle A is 79° .
By Applying the Law Of Sines ;
we get ,
[tex]\frac{SinA}{a} =\frac{SinB}{b}[/tex]
Substituting the values in the above equation ,
we get ;
[tex]\frac{Sin79\textdegree}{9} =\frac{SinB}{8}[/tex]
Simplifying further ,
we get ;
[tex]SinB = \frac{Sin79\textdegree}{9} \times 8[/tex]
substituting the value of Sin79° as 0.9816 ;
we get ;
[tex]SinB = \frac{0.9816}{9} \times 8[/tex]
[tex]SinB=0.8725[/tex]
So , B ≈ 61° .
Therefore , the measure of angle B is 61° .
The given question is incomplete , the complete question is
Find the measure of Angle B in the given figure .
Note that the angle B is acute . Round to the nearest degree .
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Use pattern blocks to represent each multiplication equation. Use the trapezoid to
represent 1 whole.
a. 3 • 1/3 = 1
b. 3 • 2/3 = 2
when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,
Describe area.The size of a region on a flat or curved surface is expressed mathematically as area. The area of a form is defined as the "space encompassed inside the perimeter or the border." The area of various shapes is calculated using mathematical methods.
given
The trapezoid's surface area is 70 units.
first base is worth 20 units, while second base is worth 10 units.
how long CE
[tex]1/2(b1 + b2)*h is the area of a trapezoid.\\70= 1/2 (20 + 10 )*h\\70 = 1/2(30)*h\\4.6 units of h[/tex]
when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,
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What is the center of a circle (x y) with the equation (x + 3)^2 + (y − 5)^2 = 16
Step-by-step explanation:
the center of the circle is (−3,5) and radius is 16 =
look at picture please
The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ
What are trigonometric identities?Trigonometric identities are equations which contain the trigonometric ratios.
How to show the equivalent identity of cot²θ + 1?Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.
So, we proceed as follows
Since cot²θ + 1 = 1/tan²θ + 1 (since cot²θ = 1/tan²θ)
Now taking the L.C.M, we have that
1/tan²θ + 1 = (1 + tan²θ)/tan²θ
We know that the trigonometric identity 1 + tan²θ = sec²θ
So, substituting this into the equation, we have that
(1 + tan²θ)/tan²θ = sec²θ/tan²θ
Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that
sec²θ/tan²θ = cot²θsec²θ
So, cot²θ + 1 = cot²θsec²θ
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a paint roller has a width of 12 inches and a radius of 3 inches, what is the surface area that can be painted with one complete rotation of the roller
The surface area that can be painted with one complete rotation of the roller is 226.19 inches².
Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.
A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.
SA = 2πrh
where SA = surface area
r = radius of the base = 3 inches
h = height of the cylinder = width = 12 inches
Plug in the values and solve for the surface area.
SA = 2πrh
SA = 2π(3 inches)(12 inches)
SA = 226.19 inches²
Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².
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Please look at image.
Answer:
Step-by-step explanation: its 90
Answer:
y=90°
since,70°+(X+X)+(180°-110°)=180°
or,70°+2X+180°-110°=180°
or,2X-40°=0
or,2X=40°
:.X=20°
Also,
X+y+70°=180°
or,y+90°=180°
:.y=90°
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If it is 10:00 A.M. Friday in Miami, Florida Eastern time zone (based on 75o W), what is time and day is it in Los Angeles California (120oW), Pacific Time zone
Therefore, the answer to the time dilemma is 7 am on Friday, which is the right choice.
Define time.In mathematics, time is described as a continuously and continuous series of events that take place in chronologically from the past through to the present and into the future. The duration of events, the gaps between them, or even the sequence of occurrences can all be quantified, measured, or compared using time.
Here,
If it is 10 a.m. on Friday in Miami, Florida's Eastern time zone, it is 7 a.m. on Friday in Los Angeles,
California's (120 o W) pacific time region
since Miami, Florida's Eastern time zone is three hours early of Los Angeles.
Thus,
the correct response is 7 am on Friday.
Therefore, the answer to the time dilemma is 7 am on Friday, which is the right choice.
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please help me
please help me
A group of 36 people from the Nantucket recreation center plans to purchase tickets for a cruise to Permut Bermuda the standard fare for an individual ticket is $1200 the group is informed that because of the size of the group the standard fare will be reduced by 30% with a discount of 30% how much does each member of the Nantucket recreation center have to pay for a cruise ticket show or explain how you got your answer (SOMEONE PLEASE HELP)
The total amount each member of the Nantucket recreation center have to pay after the discount is given by the equation A = $ 840
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount for each person after discount be represented as A
Now , the equation will be
The total number of people in the group = 36
The standard fare for each person = $ 1200
So , the total cost of the fare = total number of people x standard fare for each person
Substituting the values in the equation , we get
The total cost of the fare = 1200 x 36
The total cost of the fare = $ 43,200
Now , the discount percentage = 30 %
So , the amount after discount = total cost of the fare - total cost of the fare x discount percentage
Substituting the values in the equation , we get
The amount after discount = 43,200 - ( 30/100 ) x 43,200
The amount after discount = 43200 - 12960
The amount after discount = $ 30,240
Now ,
Total amount for each person after discount A =amount after discount / 36
Total amount for each person after discount A = 30,240 / 36
On simplifying the equation , we get
Total amount for each person after discount A = $ 840
Therefore , the value of A is $ 840
Hence , the amount is $ 840
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Please help me really fast
Answer:
Step-by-step explanation:
(0,-7) is the correct one. How I got this answer is cheese.
The ratio of the sides of a triangle is 3:5:6. If the perimeter of the triangle is 154 feet, what are the side lengths?
The side length of the triangle are
33 feet55 feet66 feetHow to find the side length of the triangleA triangle with given ratio of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of perimeter which is
= a + b + c
where
a, b, and c are the dimensions of the side length of the triangle:
Using the values given in the problem we have
let the ratio be a multiple of x such that
154 = 3x + 5x + 6x
154 = 14x
x = 11
a = 3 * 11 = 33 feet
b = 5 * 11 = 55 feet
c = 6 * 11= 66 feet
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6 the standard deviation of human body temperatures is equal to 0. 62 F. Identify the null hypothesis and alternative hypothesis in symbolic form
The null hypothesis exists that the standard deviation σ exists equivalent to 0.62. The alternative hypothesis exists that it does not equivalent 0.62.
What are null and alternative hypotheses?Statistical hypothesis testing employs null and alternate hypotheses. While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no association between variables.
A proposed claim or defense in the hypothesis test is referred to as an alternative hypothesis in statistics. In most cases, it supports the research premise and shows that there is a statistical relationship between the variables. It is one of the two statements in statistical hypothesis testing that are mutually exclusive.
H₀: σ = 0.62
H₁: σ ≠ 0.62
The null hypothesis exists that the standard deviation σ exists equivalent to 0.62.
The alternative hypothesis exists that it does not equivalent 0.62.
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Write the equation of the given function in vertex- and standard form.
f(x)
-2
2+
N
X
-1
0
1
2
3
4
f(x)
-5
0
3
4
3
0
The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4
What is a function?
A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
Given table is
x f(x)
-1 -5
0 0
1 3
2 4
3 3
4 0
Find the difference to find the degree of the given function
f(x) -5 0 3 4 3 0
1st difference 5 3 1 -1 -3
2nd difference -2 -2 -2 -2
The degree of the function is 2.
The general form of a second-degree function is
f(x) = ax²+bx+c
Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:
f(0) = a×0²+b×0+c
0 = c
Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:
f(1) = a×1²+b×1+0 [since c=0]
3 = a + b ....(i)
Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:
f(2) = a×2²+b×2+0 [since c=0]
4 = 4a + 2b ....(ii)
Solve equations (i) and (ii) by using the elimination method:
Multiply equation (i) by 2 and subtract it from (ii)
4a + 2b = 4
2a + 2b = 6
(-) (-) (-)
__________
2a = -2
a = -1
Putting a = -1 in equation (i):
-1 + b = 3
b = 3+1
b = 4
The function is f(x) = -x² +4x
Rewrite the given function in vertex form:
f(x) = -(x² - 4x +4-4)
f(x) = -(x-2)² + 4
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A whale is swimming due north at a speed of 40 kilometers per hour. Just 6 kilometers away,
a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 83
kilometers per hour. How long will it be before they meet?
Answer:
O hrs and 30 minutes is the answer
Step-by-step explanation:
want proof?
Answer:
about 0.04878 hours ≈ 2 minutes 56 seconds
Step-by-step explanation:
You want the time until a whale-watching boat and a whale meet if the boat is traveling south at 83 km/h and the whale is traveling north at 40 km/h when they start 6 km apart.
Closing speedThe speed at which the gap between the boat and the whale is closed is the sum of their respective speeds:
closing speed = 83 km/h + 40 km/h = 123 km/h
TimeThe time it takes to close the 6 km gap is ...
time = distance/speed
time = (6 km)/(123 km/h) ≈ 0.04878 h
Converted to minutes and seconds, that is about ...
0.04878 h ≈ 2 minutes 55.6 seconds
It will be about 2 minutes 56 seconds before the boat and whale meet.
__
Additional comment
NOAA recommends a distance of at least 100 yards be maintained between a boat and a whale. In some areas, the recommended distance is 400 yards when approaching head-on. The recommended boat speed is 15 knots or less, about 28 km/h.
The scale drawing of a building has a height of 10 centimeters. The actual building is 20 feet high. How many centimeters in the scale drawing represent one foot on the actual building?
a. 1/2
b. 30
c. 10
d. 2
Answer: 1/2
Step-by-step explanation:
The question is asking you to find how many centimeters in the scale drawing equal 1 foot on the actual building. The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter, or A.
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pls solve me this functions question
On solving the provided question, we can say that - the value of the function is f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]; f(x) = x= it doesn't factor
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
f(x) = [tex](x+3)^2 - 5[/tex]
f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]
f(x) = x= it doesn't factor
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Find the total surface area of this cuboid.
5 cm
4 cm
6 cm
Answer: 15cm2
Step-by-step explanation:
5cm+4cm+6cm=15cm2
1)
2)
Which relation is not a function?
1
-A
30
2
B
3.
: mo
C
A
4
36
3
3)
4)
2-
x
relations
246
6:
8-
Co
8
-10
12
₹10
12
Answer:
2, cause it shows a different function or pattern
- 3 (x + 8) ^ 2 - 3
Answer:
-3x + 549
Step-by-step explanation:
The order of operations is PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction)
So, according to PEMDAS, the first thing that we would do is solve the parenthesis. Since we can't solve the parenthesis because they aren't like terms, we're going to use distributive property to solve it instead.
-3(x+8) = -3(x) + -3(8) = -3x -24
Now we have: -3x - 24 ^ 2 -3
Our next step is to solve the exponent
24 ^ 2 or 24 x 24 = 576
Now we have: -3x - 24 + 576 -3
Our next step would be to add and subtract the like terms
-24 + 576 = 552 and 552 - 3 = 549
Now we have: -3x + 549
This would be the simplest form of the equation because -3x and 549 are not like terms
Tommy earned $225 washing cars with his mobile car washing business. He charges $30 per appointment and earned $45 in tips, but he also has to pay $10 per appointment for water. Write an equation to represent this situation.
A.
(30 + 10)y + 45 = 225
B.
30y + 45 = 225 - 10y
C.
30y + 45y - 10y = 225
D.
(30 - 10)y + 45 = 225
An equation representing this situation where Tommy earned $225 washing cars per appointment charge of $30 and tips of $45 while paying $10 for water per appointment is D. (30 - 10)y + 45 = 225.
What is an equation?An equation is a mathematical statement that states that two or more mathematical expressions are equivalent or equal.
Equations depict the equality of mathematical expressions using the equation symbol (=).
The total amount earned = $225
Variable charge per appointment = $30
Tips earned = $45
Variable cost per appointment for water = $10
Contribution margin per unit = $20 ($30 - $10)
Let each appointment = y
Total earnings: 225 = (30 - 10y) + 45
Thus, the equation that represents the situation of Tommy's net earnings from washing cars is Option D.
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Use Pascal's Triangle to expand (5z + 5x²)³. Express your
answer in simplest form.
The simplest form is 15z+ 15x²
How to simplify the given expression ?In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)n. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.
Because it has so many patterns that can be used to greatly simplify complex calculations, Pascal's triangle is significant.
Given,
(5z+5 x²)3
15z+15x² by simplifying,
3(5z+5 x²)
apply the distributive formula :a (b + c) =ab + ac
3(5z+5 x²) = 5x+3 * 5x²
By simplifying 3 5z+3 , 5x², 15z+15x²
we get
15z+ 15x²
Therefore the simplest form is 15z+ 15x² .
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43 inches tall. Each book 1/2 - inch thick
Answer:
If you're asking how many books there are its 86.
Step-by-step explanation:
If each book is 1/2 thick that means there are 2 books per inch.
Because there are 43 inches you're going to multiply by 2.
43(2)= 86.
Hope that helped, have a good day!