The number of points of intersection for the graphs of the equations is infinite.
Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.
Simplifying the given equations:
i) x/2 + 5y = 6
x + 10y = 12
ii) 3x + 30y = 36
3(x + 10y) = 36
x + 10y = 12
As the equations are equal lines, they will intersect at infinite times.
Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many
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when a hot object is placed in a water bath whose temperature is 25∘c, it cools from 100∘c to 50∘c in 180s. in another bath, the same cooling occurs in 160s. find the temperature of the second bath.
the sum of yhe age ofa father and his son us 50 years if the ages of the is 10 years. find the age of the father
Which of the following equations has 2 as a root? (a) `x^(2)-4x+5=0`, (b) `x^(2)+3x-12=0`
(c) `2x^(2)-7x+6=0`, (d) `3x^(2)-6x-2=0`
The given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Ax+By=C is the usual form for two-variable linear equations.
A standard form linear equation is, for instance, 2x+3y=5.
(A) x² - 4x + 5 = 0
LHS: x² - 4x + 5
= (2)² - 4(2) + 5
= 4 - 8 + 5
= -4 + 5
= 1
RHS = 0
LHS ≠ RHS
Has no root that is 2 in it.
(B) x² + 3x - 12 = 0
LHS: x² + 3x - 12
= (2)² + 3(2) - 12
= 4 + 6 - 12
= 10 - 12
= -2
RHS = 0
LHS ≠ RHS
Has no root that is 2 in it.
(C) 2x² - 7x + 6 = 0
Put x = 2
= 2(2)² - 7(2) + 6
= 8 - 14 + 6
= 14 - 14
= 0
RHS = 0
LHS = RHS
It has 2 roots.
(D) 3x² - 6x - 2 = 0
LHS: 3x² - 6x - 2
= 3(2)² - 6(2) - 2
= 12 - 12 - 2
= -2
RHS = 0
LHS ≠ RHS
Has no root that is 2 in it.
Therefore, the given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.
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Write a polynomial function that meets the stated condition.
The zeros are -2/3 and , and the constant term of the polynomial is -10.
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.
How to get polynomials with zeroes?Let a, b, c, and d are the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
The zeros are -2/3. Then the factor of the polynomial is given as,
x = - 2/3
3x = - 2
3x + 2 = 0
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be given as,
p(x) = 3x + 2 - 10
p(x) = 3x - 8
The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.
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what is the sum of the rational expressions below? 3x/x 2
The rational expression is 4x² - 3x /(x + 9)(x -4).
How do you sum rational expressions?A ratio of two polynomials defines a rational expression. When adding or subtracting two rational expressions with the same denominator, we simply add or subtract the numerators and write the outcome over the shared denominator.The sum of the following rational expression is supplied to us, and we are to discover it:3x / x +9 + x (x -4)
3x / x +9 = 3x (x -4)/(x + 9)(x -4)
x / x - 4 = x(x +9)/(x - 4 )(x + 9)
3x (x - 4)/(x + 9)(x - 4) + x(x + 9)/(x - 4 )(x + 9)
3x (x -4 ) + x (x - 9) / (x + 9)(x - 4)
4x² - 3x / (x + 9 ) (x - 4).
The Complete Question is Rational Expression.
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Answer:
The sum of the rational expressions is 4x² - 10x / (x + 2 ) (x - 4)
What are rational expressions?
A rational expression is defined by the ratio of two polynomials.
We simply add or subtract the numerators and write the result over the shared denominator when adding or subtracting two rational expressions with the same denominator.
According to question:
Solving 3x/x + 2 + x/(x -4)
The sum of the following rational expression is supplied to us, and we are to discover it:
⇒ 3x / x +2 = 3x (x -4)/(x + 2)(x -4)
⇒ x / (x - 4)= x(x +2)/(x - 4 )(x + 2)
3x (x - 4)/(x + 2)(x - 4) + x(x + 2)/(x - 4 )(x + 2)
(3x (x -4 ) + x (x + 2)) / (x + 2)(x - 4)
4x² - 10x / (x + 2 ) (x - 4).
hence, the sum of the rational expressions is 4x² - 10x / (x + 2 ) (x - 4).
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The Complete Question is
what is the sum of the rational expressions below?
3x/x + 2 + x/(x -4)
Quadrilateral STUV is similar to quadrilateral WXYZ. Find the measure of side XY.
Figures are not drawn to scale.
Answer:
11.4
Step-by-step explanation:
Given these quadrilaterals are similar, all we have to do is divide 21 (ST) by 5.7 (WX). That should give us 3.6842105263, which is the scale factor. To find the length of XY, we have to divide UT (the side similar to XY) by the scale factor. UT = 42, and 42/3.6842105263 = 11.4
Answer:
11.4
Step-by-step explanation:
please help me ( I will give brainlist for correct answer)
Using the concept of unit price, we see that;
Unit price of Brand A = $0.3654
Unit price of Brand B = $0.3785
The better buy is Brand A
How to find the unit price?A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can then be used to compare the same type of goods sold in differing weights and amounts.
Now, we are told that brand A has a pack of 24 pencils for $8.77. Thus;
Unit price of Brand A = 8.77/24 = $0.3654
We are told that brand B has a pack of 26 pencils for $9.84. Thus;
Unit price of Brand B= 9.84/26 = $0.3785
Thus;
Unit price of Brand A = $0.3654
Unit price of Brand B = $0.3785
Thus, brand A has the cheaper unit price and is thus the better buy.
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suppose that in the sample, 55 students said that they recycle. is this convincing evidence that more than half the students at the school would say they regularly recycle?
It is insufficient proof that more than half of the students at the school recycle.
Given :
suppose that in the sample, 55 students said that they recycle.
It is insufficient proof that more than half of the students at the school recycle because: "Yes" was replied by 55 out of 100 pupils.
= 55 / 100
= 0.55
We can see that the proportion 0.55 of has a lot of dots above it in the dot plot.
As a result, a proportion of 0.55 is quite likely to be obtained when the genuine proportion is 0.5, and there is insufficient evidence to support the assertion that more than half of the school's students recycle.
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working together, it takes two different sized hoses 40 minutes to fill a small swimming pool. if it takes 60 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.
Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40
Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60
Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60
The amount of swimming pool filled in 1 minute = (60 - 40)/2400
The amount of swimming pool filled in 1 minute = 20/2400
The amount of swimming pool filled in 1 minute = 1/120
Total time taken to fill swimming pool = 1 ÷ (1/120)
Total time taken to fill swimming pool = 120 minutes
Thus, 120 minutes are required.
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This design began from the construction of a regular hexagon.
Select all true statements about quadrilateral JKLO.
1.) When JKLO is reflected across segment OA, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
2.) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
3.) When JKLO is reflected in any way, it will not produce another congruent quadrilateral in this figure. However, there is a way to translate JKLO to take it to another quadrilateral in this figure.
4.) When JKLO is reflected across segment OI, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
5.) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
The statement 2) and 5) about the construction are correct.
What is construction?In geometry, the term "construction" refers to precisely drawing forms, angles, or lines. These structures simply require a pencil, compass, and straightedge (a ruler).
Given this, a design was created by building a standard hexagon.
The construction's real claims are as follows:
2) JKLO is taken to JIHO when it is mirrored across segment OJ. Therefore, quadrilateral JKLO and quadrilateral JIHO are congruent.
5) JKLO is transferred to HGLO when it is reflected over segment OL. Therefore, quadrilateral JKLO and quadrilateral HGLO are congruent.
Therefore, statement 2 and 5 about the structure are true.
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How do you solve 2=11+3(m+3)?
Answer: m= -6
Step-by-step explanation: 2 = 11 + 3m + 9
3m = 2 - 11 - 9
3m = -18
Divide both sides by 3.
m= -6
Answer:
m = -6
Step-by-step explanation:
Step by step explanation:
2-11 = 3m+9 ==》3m = -18 ==》m = -18/3 ==》m= -6
! if f( n + 1) = f(n) + 2 and f(2) = 4 then f(4) =
explain
Answer: 8
Step-by-step explanation:
From our knowledge, we know two things.
f(n + 1) = f(n) + 2f(2) = 4From here, we can work out what f(3) is by substituting n as 2
f(2 + 1) = f(2) + 2
f(3) = 4 + 2 = 6
And we can work out f(4) by substituting n as 3
f(3 + 1) = f(3) + 2
f(4) = 6 + 2 = 8
Eventually, if you continue doing this, you will see a sequence forming where the next number is the previous number added by 2.
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 17
cubic feet. There were twice as many large boxes shipped as small
boxes shipped and the total volume of all boxes was 258 cubic feet.
Determine the number of small boxes shipped and the number of large
boxes shipped.
There were __?_
small boxes shipped and __?_
large boxes shipped.
Answer:
9 small boxes and 15 large boxes
Step-by-step explanation:
x = small box
y = large box
x + y = 24
9x + 24y = 441
-9x - 9y = -216
15y = 225
y = 15
x + 15 = 24
x = 9
Find domain and range please! Also, due tmrw!
The Domain of the Function is {-2, -1, 0,1 ,2, 3, 4, 5} and the Range of the Function is {4, 3, 2, 1, 0, -1}
What are Functions?
A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
Solution:
We neeed to find the Domain and Range of the Function
Domain refers to all the values of x = {-2, -1, 0,1 ,2, 3, 4, 5}
Range refers to all the values of y = {4, 3, 2, 1, 0, -1}
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Solving the linear system of equations using elimination.
8x - 6y= -20
-8x + 4y = 24
Answer:
j
Step-by-step explanation:
Answer:
the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.
Step-by-step explanation:
To solve a system of linear equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the variable x.
The given equations are 8x - 6y = -20 and -8x + 4y = 24. We can add these equations by aligning the like terms and then combining them. This gives us:
8x - 6y = -20
-8x + 4y = 24
-16x + 8y = -20 + 24
-16x + 8y = 4
Dividing both sides of the equation by 8, we get:
-2x + y = 1/2
Therefore, the solution to the system of equations is x = -1/2 and y = 1/2.
We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -1/2 and y = 1/2 into the first equation, we get:
8(-1/2) - 6(1/2) = -20
-4 - 3 = -20
-7 = -20
This is not a true statement, so our solution is not correct.
One mistake we made was adding the equations instead of subtracting them. If we subtract the second equation from the first equation, we get:
8x - 6y = -20
-8x + 4y = 24
8x - 6y - (-8x + 4y) = -20 - 24
2x - 2y = -44
Dividing both sides of the equation by 2, we get:
x - y = -22
Therefore, the solution to the system of equations is x = -22 and y = -22.
We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -22 and y = -22 into the first equation, we get:
8(-22) - 6(-22) = -20
-176 + 132 = -20
-44 = -20
This is a true statement, so our solution is correct. Similarly, plugging x = -22 and y = -22 into the second equation, we get:
-8(-22) + 4(-22) = 24
176 - 88 = 24
88 = 24
This is also a true statement, so our solution is correct. Therefore, the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.
Mark transferred songs from his computer onto his portable music player. He transferred 2 6/7 songs in 1 2/3 minutes. How many songs did he transfer per minute?
A. 7/12 song per minute
B. 1 5/7songs per minute
C. 2 2/3 songs per minute
D.4 16/21 songs per minute
The number of songs that he transferred per minute is 1 5/7 songs per minute (option B).
How many songs did he transfer per minute?In order to determine the number of songs he can transfer in one minute, divide the number of songs transferred in 1 2/3 by the number of minutes.
Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal groups using another number. The sign that is used to represent division is ÷
Number of songs they want to transfer per minute = 2 6/7 ÷ 1 2/3
20 /7 ÷ 5/3
20/7 x 3/5 = 12/7 = 1 5/7 songs per minute
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21. A virus reproduces by tripling every half hour. If a single virus gets into your system and continues at this rate, how much of it will be in your system after a 24-hour period. (Hint: there would be two instances of tripling after the first hour) 24 hours
Please this is urgent need within 20-30 mins
Answer:
Not 100% sure but I believe the answer is 110592.
Step-by-step explanation:
48^3= 110592
Write an equivalent expression by using the distributive property.
a. 2(3x+5)
b. 7(7a+6)
c. Sa(4a+8b)
d. 2y(4x-3y)
e. 3z(9-10z)
f. 6(3x+4+2y)
g. 11c(2c+7a)
h. 8b(5+2s+3b²)
i. 7a(a²-3a+6)
j. 9(4p²+3p-5)
The equivalent expression of each expression given, using the distributive property, are:
a. 6x + 10
b. 49a + 42
c. 20a² + 40ab
d. 8xy - 6y²
e. 27z - 30z²
f. 18x + 24 + 12y
g. 22c² + 77ac
h. 40b + 16bs + 24b³
i. 7a³ - 21a² + 42a
j. 36p² + 27p - 45
What is the Distributive Property?If we have an expression given as a(b + c), according to the distributive property, we can write an equivalent expression by using the term "a" to multiply each of the terms within the bracket, which will give us: a(b + c) = ab + ac.
a. 2(3x + 5), applying the distributive property, multiply each of the terms within the parentheses by 2:
2(3x) + 2(5)
6x + 10
Therefore, the equivalent expression of 2(3x + 5) is 6x + 10.
b. 7(7a+6)
7(7a) + 7(6)
= 49a + 42
c. 5a(4a+8b)
= 5a(4a) + 5a(8b)
= 20a² + 40ab
d. 2y(4x-3y)
= 8xy - 6y²
e. 3z(9 - 10z)
= 27z - 30z²
f. 6(3x + 4 + 2y)
18x + 24 + 12y
g. 11c(2c + 7a)
22c² + 77ac
h. 8b(5 + 2s + 3b²)
40b + 16bs + 24b³
i. 7a(a² - 3a + 6)
7a³ - 21a² + 42a
j. 9(4p² + 3p - 5)
36p² + 27p - 45
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graph the line that passes through the points (0,-8) and (5,-5) and determine the equation of the line
*I can graph it, I just need the equation*
The linear equation that passes through the points (0,-8) and (5,-5) is:
y = (3/5)*x - 8
How to find the equation of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we have the two points: (0,-8) and (5,-5)
Then the slope is:
a = (-5 + 8)/(5 - 0) = 3/5
And because of the point (0, -8) we know that the y-intercept is -8, then the linear equation is:
y = (3/5)*x - 8
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10 grams is the same as how many ounces?
The value of the one-gram quantity in ounces will be 0,35274 ounces.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the quantity of some materials is measured in 10 grams. The quantity of the material in ounces will be calculated as,
1 grams = 0.035274
10 grams = 10 x 0.035274
10 grams = 0.35274 ounces
Therefore, the value of the one-gram quantity in ounces will be 0,35274 ounces.
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what is the value of p
The value of p is 18, it can be find out by using concepts of line and slope of a line.
What is the slope of a line?
Slope of line measures its steepness. Mathematically, its calculated as "rise over run".
Slope of a line : (y2 - y1)/(x2-x1)
In the given que,
given graph equation is of line ,
to find slope of graph : we need to differentiate the equation
[tex]\frac{d}{dx}[/tex](3y + 2x = 7) = 3[tex]\frac{dy}{dx}[/tex] + 2 = 0
So, [tex]\frac{dy}{dx}[/tex] = -2/3
We, if any line are perpendicular then
slope of one * slope of two = -1
So, slope of 1 = (-9-6)/(8-p)
= -15/(8-p)
slope of 2 = -2/3
Now product of both = -15/(8-p) * (-2/3 )
By simplifying all these equation,
we get p = 18.
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Which of the following is a equation of x-axis 1)y-0. 2)x-0. 3)x-0. 4)y-0
Answer:
none of the listed options
Step-by-step explanation:
the equation for x axis is y=0
If a building contractor hires 8 day laborers and 2 concrete finishers, his payroll for the day is $1464. If he hires 1 day laborer and 5 concrete finishers, his daily cost is $943. Find the daily wage for each type of worker. Solve the problem using matrices.
The day worker's daily compensation is $160, while the concrete finisher's daily wage is $143.
What is matrices?A matrix is a numerical arrangement that is divided into rows and columns. Introduce yourself to matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a collection of integers that are organized in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.
Here,
Let x be the Charge for day labor and y be the charge for concrete finisher,
8x+2y=1464
x+5y=943
multiply x+5y=943 by 8,
8x+40y=7544
8x+2y=1464
subtracting them,
38y=6080
y=$160
x+5*160=943
x=943-800
x=$143
The daily wage for day worker is $160 and the daily wage for concrete finisher is $143.
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What is the input value for which g(x) = 3?
At the Input Value 9 the function g(x) will be 3.
What are Function?
A function in mathematics from a set X to the a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Al-Biruni as well as Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest known treatment of the concept of function. Initially, functions represented the idealised relationship between two varying quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with infinitesimal calculus just at end of the seventeenth century, and indeed the functions that were taken into consideration were differentiable until the 19th century.
Solution:
So, it can be observed from the graph that g(x) = 3
when the value of x is 9
So, the input value is 9.
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An arithmetic sequence has first term 13 and common difference 6. Find the 25th term
of the sequence.
Answer:
a₂₅ = 157
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 13 and d = 6 , then
a₂₅ = 13 + (24 × 6) = 13 + 144 = 157
There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh
graders, and the rest are eighth graders.
How many band members are seventh graders?
Answer:
14
Step-by-step explanation:
10 percent of 70 is 7
20 percent of 70 is 14
So 14 is your answer
Please vote brainliest
Thanks
Have a nice evening
Answer: All you would have to do is multiply 70 by 20% which is 14. So 14 7th graders are a total of the band.
Step-by-step explanation:
Solve the equation.
4/7 = 10/X
x=
Answer:
x = 17.5
Step-by-step explanation:
4/7 = 10/X
We can use cross products to solve for x
4*x = 7 * 10
4x = 70
Divide by 4
4x/4 = 70/4
x = 17.5
Answer:
17.5
Step-by-step explanation:
[tex] \frac{4}{7} = \frac{10}{x} \\ [/tex]
Use cross multiplication.
4x = 7 × 10
4x = 70
Divide both sides by 4.
x = 70/4
x = 17.5
(a)The perimeter of a rectangular parking lot is 350 m . If the length of the parking lot is 97 m , what is its width?
The width of the parking lot is 78 m
We have been given the perimeter of a rectangular parking lot which is equal to 350 m.
We know the perimeter of a rectangular plot is 2 X (width of the plot ) + 2 X (length of the parking lot ).
And the length of the parking lot is given as 97 m.
2 X (width of the plot ) +2 X (length of the parking lot ) =350 m
2 X (width of plot ) + 2 X 97 =350
2 X (width of the plot ) =156 m
width of the plot = 78 m
Hence the width of the plot is 78 meters.
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The width of this rectangular parking lot is equal to 78 meters.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following:
P = 2(L + W)
350 = 2(97 + W)
175 = 97 + W
Width, W = 175 - 97
Width, W = 78 meters.
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The area of a rectangle is 215.1 m². If the length is 18 m, what is the perimeter of the
rectangle?
Answer: 59.9 m
Step-by-step explanation:
Area of rectangle = Length times Width
We already know the length is 18m
So take 215.1 divided by 18= 11.95m
To find the perimeter of the Rectangle we use the formula
p= 2(18+ 11.95) = 59.9 m
So the perimeter is 59.9 m
HELPP!!!
angles of a triangle
Math
help please! Thank u.
Answer:Try 81
Step-by-step explanation:
a sector of a circle has a central angle of 120 ∘ . find the area of the sector if the radius of the circle is 20 cm.
Answer:
A ≈ 418.9 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{120}{360}[/tex] ( r is the radius )
= π × 20² × [tex]\frac{1}{3}[/tex]
= [tex]\frac{400\pi }{3}[/tex]
≈ 418.9 cm² ( to the nearest tenth )
