Identify whether each system of equations has infinitely many solutions or no solution.
The first system of equations has no solution and the second set of equations has a unique solution.
If we are having two equations as
[tex]a_{1} x^{2} +b_{1} x+ c_{1} =0[/tex]
and [tex]a_{2} x^{2} +b_{2} x+ c_{2} =0[/tex]
The condition at which these equations will have infinitely many solutions is
[tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } =\frac{c_{1} }{c_{2} }[/tex]
The condition at which these equations will have infinitely many solutions is
[tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]
For, the 26th question, we have
4x +8y = -8
4x +8y +8 = 0
x +2y +2 =0 equation(1)
x =-2y +1
x +2y -1 = 0 equation(2)
On comparing these equations with the general form, we have
[tex]a_{1} = 1, a_{2} =1\\b_{1} = 2, b_{2} = 2\\c_{1} = 2, c_{2} = -1[/tex]
So, [tex]\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }[/tex]
Thus, this system of equations has no solution.
Now, For the 27th question, we have
2x - 3y = 6
2x -3y -6 = 0 equation(3)
[tex]y = \frac{2}{3}x -2 \\\\3y = 2x -6\\\\3y -2x +6 = 0[/tex] equation (4)
On comparing these equations with the general form, we have
[tex]a_{1} = 2, a_{2} =3\\b_{1} = -3, b_{2} = 2\\c_{1} = -6, c_{2} = 6[/tex]
So, [tex]\frac{a_{1} }{a_{2} } \neq \frac{b_{1} }{b_{2} }[/tex]
Thus, this system of equations has a unique solution.
To read more about the system of equations, visit https://brainly.com/question/24065247
#SPJ1
Find the slope and y-intercept of the graph of the linear equation. Write your answers in simplest form.
y=9.5
Slope: ?
y-intercept: ?
Answer:
0, 9.5
Step-by-step explanation:
We can rewrite the equation as [tex]y=0x+9.5[/tex].
Comparing this to slope-intercept form, the slope is 0 and the y-intercept is 9.5.
What does the transformation f(x)—>f(1/3x) do to the graph of f(x)?
The transformation f(x)—>f(1/3x) due to the graph of f(x), will be dilation horizontally and vertically.
What is Transformation of Function?
Transformation of functions refers to the graph's curve moving to the left, right, up, or down, expanding, contracting, or reflecting. Just dilation, out of these three transformations, alters the size of the original shape; the other two only adjust the position.
A translation happens when each point on a graph (which represents a function) travels in the same direction and by the same amount. There are two kinds of function translations.
Stretching or compressing is a dilation. The x-values on a graph are all scaled up by the same amount when a dilation that is parallel to the x-axis occurs. The y-values are all increased by the same scale factor if it is dilated parallel to the y-axis.
f(x) to become f(1/3x), Then it will go dilation "vertically and horizontally".
Referring to the graph mentioned below we can conclude the same.
Learn more about Transformation, by the following link.
brainly.com/question/24349828
#SPJ1
Write down two expressions for the
perimeter of this shape, one with
brackets and one without.
t + 5
P (with brackets) =
P (without brackets) =
[2]
[2]
The expression for the perimeter of the square with and without brackets is 4(t + 5) and 4t + 20, respectively.
We are given a shape. The shape is a square. The side length of the square is equal to (t + 5). We have to find the expression for the perimeter of the square. A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. Let the perimeter of the square be denoted by the variable "P".
The expression for the perimeter of the square in brackets is given below:
P = 4(t + 5)
The expression for the perimeter of the square without brackets is given below:
P = 4t + 20
To learn more about perimeter, visit :
https://brainly.com/question/6465134
#SPJ1
What are the missing values?
The ratio table's missing values are 6: 3, 24:12, and 18:9.A ratio shows how many of one number there are of another. Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.
What does ratio mean?A ratio shows how many of one number there are of another. Two numbers are expressed as x: y, which is equivalent to x/y, to represent their ratio.
where each of the two variables, x and y, is a separate quantity.
Additionally, the combined total is given as x + y.
Therefore, Peoples = 6, 18 and Benches = 3, 12
Now,
These ratios are equivalent: 6: 3, x: 12, and 18: y.
Ascertain the values of x and y.
Given that all ratios are equal.
so we obtain;
⇒ 6 : 3 = x : 12
⇒ 6 / 3 = x / 12
⇒ 6 × 12 / 3 = x
⇒ x = 24
And, ⇒ 6 : 3 = 18 : y
⇒ 6 × y = 18 × 3\s⇒ y = 18 × 3 / 6\s⇒ y = 9
Therefore, the ratio table's missing values are 6: 3, 24:12, and 18:9.
To learn more about Ratio refer to:
https://brainly.com/question/2914376
#SPJ1
F(x)=x² + 7
Find
a) F (10)
6) F(-3)
The value of f(10) = 107 and f(-3) = 16.
The function is defined as in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). An example of this would be y=x2. You only get one output for y if you enter anything for x. Considering that x is the input value.
Given that f(x)=x² + 7
We do determine the values of F (10) and F(-3)
Now f(10)
= (10)2 +7
= 100 +7
= 107
Now f(-3)
= (-3)2 +7
= 9 +7
= 16
Therefore the value of f(10) = 107 and f(-3) = 16
To learn more about functions visit
https://brainly.com/question/14606675
#SPJ9
explain what the symbols and sd represent.
The symbols d and sd represent:
The differences in the mean of the paired data entries in the dependent samples.
What is the standard deviation?
A measure of a set of values' variance or dispersion is called the standard deviation.
Here,
d: the difference between paired data in the dependent samples.
sd: standard deviation.
The dependent samples' dependent samples' standard deviation for the variance between the means of the paired data items.
Hence, the differences in the mean of the paired data entries in the dependent samples.
To learn more about the standard deviation from the given link
https://brainly.com/question/475676
#SPJ4
based on the information given above is it possible to compute the probability that a randomly selected cookie has a weight less than 14 g?
0.1367 percent of randomly chosen cookies will weigh less than 14 grams.
Given data;
Is it possible to calculate the likelihood that a randomly selected cookie weighs less than 14g using the information provided above?
Let,
X = Average cookie weight in a pack of 30
E (X) = μ = 15
Var (X) = σ²/n
= 1²/30 = 0.0333
⇒ Standard Deviation (X) = √0.0333 = 0.1826
P(X ≤ 14.8) = (X-15 / 0.1826 < 14.815/0.1826)
= P(14.815 - 0.1826)
= P(Z-1.1)
= 0.1367
Hence, the probability that a randomly selected cookie has a weight less than 14g is 0.1367
To learn more about probability click here:
brainly.com/question/11234923
#SPJ4
Convert 47 grams to ounces. (1 gram = 0.0352 ounce)
A: 0.0007 ounce
B: 1.6544 ounces
C: 16.544 ounces
D: 1,335.23 ounces
Answer:
1.6544 ounces
Step-by-step explanation:
47x0.0352
1.6544 ounces
Hopes this helps please mark brainliest
ASAP! exponent rules
Answer: P and Q could both be equal to -1
A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
Question 3 options:
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line x = 0 is an asymptote of the graph.
The point (0,30) contains the x-intercept.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
The asymptote indicates that there were never more than 800 mice in existence.
The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0 thus option (A),(B), and (E) is correct.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
The given graph of the number of mice in the number of weeks the cat adopted.
The asymptote of the graph is y = 0.
The asymptote tells that the number of the mouse will become zero when the number of cats becomes infinite.
Hence "The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0".
To learn more about graphs,
brainly.com/question/24861666
#SPJ1
What is the equation of the line that passes through the points (5,3) and
(5,-2)?
Answer:
x = 5
Step-by-step explanation:
I'm going to assume that this is asking you to graph in Slope-Intercept form, but if I am mistaken, comment on my answer and I will happily change it.
Slope-Intercept form:
y = mx + b
You leave y and x as variables, while m and b are to be substituted for slope and y-intercept. y-intercept is when x=0, where a point on a line is on the y axis.
To help you learn, for example, we have an equation is slope-intercept form:
y = 8x + 3
In this case, the slope is 8 and the y intercept is 3 as m is the slope and b is the y-intercept.
The slope is the steepness of the graph. The value of the slope is how much the y-value increases if the x-value increases by 1.
We can find the slope from 2 points using this formula:
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we plug in our points into the formula.
[tex]\frac{-2-3}{5-5}[/tex]
Simplify.
[tex]\frac{-5}{0}[/tex]
Anything divided by 0 is undefined. This means the line we are graphing is completely vertical, known as undefined. We can only get this if the x value stays the same no matter what. In this case, the x value stays the same when the y value changes, meaning a undefined slope.
We have a special case here. If the slope is undefined, we do not use y = mx+b. Instead, we use:
x = what the x values of the 2 points are
x values of both points: 5
x = 5
I will name you the Brainliest if you answer!
Choose the ordered pair that is a solution of the inequality y ≤ −3x − 5.
(2, 3)
(0, 0)
(−1, −3)
(0, −1)
Answer:C. (1,-3)
E. (2,5)
Step-by-step explanation:
Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars. 0.8d Choose... d – 0.2 Choose... d – 0.2d Choose... 1 – 0.2d Choose...
The expression that represents a 20% discount off the price of an item that originally cost d dollars include:
0.8d
d - 0.2d
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the cost of the item is d. Since there's a 20% discount, the new cost will be:
= d - (20% × d)
= d - 0.2d
= 0.8d
The cost is 0.8d.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?
Answer:
0
Step-by-step explanation:
153 isn't between 1-100 making the probability 0
Find the sum of the interior angle measures of a regular polygon with 19 sides.
Answer:
Step-by-step explanation:
3060
solve for y and then graph the solution: -25 < 4y + 3 < 19
So, for this question, there are two answers possible that you could put in.
-25 < 4y + 3 < 19 in inequality form: -7<y<4
-25 < 4y + 3 < 19 in interval notation form: (-7,4)
The graph that goes alongside it should be attached to this answer as well.
Hope this helps! :)
A farmer grows 128 red tomatoe plants and 102 yellow tomato plants each plants about 32 tomatoes the farmer plants to sell each tomatoes for $2 explain how to find a reasonable as the meal for the total of money is the farmers market
The total amount of money that farmer will make to sell the tomatoes for $2 per tomato will be $14720.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Multiplication = to multiply any two or more numbers or variables called multiplication.
The number of red tomato = 128 × 32
The number of yellow tomato = 102 × 32
The total cost will be,
2(128 × 32) + 2(102 × 32)
⇒ 2(4096) + 2(3264)
⇒8192 + 6528
⇒$14720
To learn more about the arithmetic operators,
brainly.com/question/25834626
#SPJ1
PLS HELP URGENT!!!
Q.1: (Q.1 IN FIRST IMAGE!!)
The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select EACH correct answer.
Question 1 options:
The y-intercept represents the number of mammals when they were originally counted.
The line y = 0 is an asymptote of the graph.
The y-intercept.is 75.
The y-intercept is 120.
The asymptote indicates that the number of mammals counted when the study began was 120.
The asymptote indicates that as years pass, the number of mammals will approach 0.
The line x = 0 is an asymptote of the graph.
Q.2 ( IMAGE IN SECOND )Once an antibiotic is given, number of bacteria decreases at a rate of 15%/day. There were about 15,000 bacteria prior to the treatment. The graph models the number of bacteria after x days of treatment.
What are the key features of the exponential function modeled in terms of this situation and how can they be interpreted?
Select each correct answer.
Question 2 options:
The line y = 0 is an asymptote of the graph.
The x-intercept is 30.
The line x = 0 is an asymptote of the graph.
The asymptote indicates that there will never be more than 15,000 bacteria.
The y-intercept is 15,000.
The y-intercept represents the number of bacteria when treatment began.
The asymptote indicates that as time increases, the number of bacteria approaches 0.
Q.3 ( Q.3 IN THIRD IMAGE) A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
The features for each of the exponential functions are listed as follows:
1.
The y-intercept represents the number of mammals when they were originally counted.The line y = 0 is an asymptote of the graph.The y-intercept is 120.The asymptote indicates that as years pass, the number of mammals will approach 0.2.
The line y = 0 is an asymptote of the graph.The y-intercept is 15,000.The y-intercept represents the number of bacteria when treatment began.The asymptote indicates that as time increases, the number of bacteria approaches 0.3. The key features are listed as follows:
y-intercept of 800, which is the number of mice when the study began.The line y = 0 is the asymptote of the graph, indicating that as the number of weeks increase, the number of mice approaches 0.What are the features of exponential functions?The features to the graphs of the exponential functions are listed as follows:
y-intercept: Initial value of the output variable, that is, the value of y when the function crosses the y-axis.horizontal asymptote: value that the output variable approaches as the input variable goes to infinity.More can be learned about exponential functions at
https://brainly.com/question/25537936
#SPJ1
2x + 3y = 30 solve for y
change each decimal to fraction then determine whether the decimal is terminating.
1. 2
8
2. 8
10
3. 1
6
4. 4
9
5. 8
11
6. 14
11
7. 3
7
Answer:
ok ask your teacher
Step-by-step explanation:
solving with master product 3x^2-17x+10=0
In a class of 80 students, 40 study physics, 48 study mathematics and 44 study chemistry. 20 study physics and mathematics, 24 study physics and chemistry and 32 study only two of the three subjects. If every student studies at least one of the three subjects, find : a. The number of students who study all the three subjects. b.The number of students who study only mathematics and chemistry.
1. The number of students who study all three subjects is 10.
2. The number of students who study only mathematics and chemistry is 8
What are set operations?Set operations are the operations that are applied on two or more sets to develop a relationship between them.
Let mathematics = M, physics = P, chemistry = C.
n(M∪P∪C) = 80
n(M) = 48
n(P) = 40
n(C) = 44
n(M∩P) = 20
n(M∩C) = ?
n(C∩P) = 24
n(M∩P) + n(M∩C) + n(C∩P) - 3n(C∩P∩M) = 32
20 + n(M∩C) + 24 - 3n(C∩P∩M) = 32
n(M∩C) = 3n(C∩P∩M) - 12 - *
We know,
n(M∪P∪C) = n(M) + n(P) + n(C) - n(M∩P) - n(M∩C) - n(C∩P) + n(C∩P∩M)
80 = 48 + 40 + 44 - 20 - n(M∩C) - 24 + n(C∩P∩M)
n(M∩C) = n(C∩P∩M) + 8 -
Equating
n(C∩P∩M) + 8 = 3n(C∩P∩M) - 12
2n(C∩P∩M) = 20
n(C∩P∩M) = 10
Putting the value of n(C∩P∩M) in *
n(M∩C) = 18
n(M∩C) - n(C∩P∩M) = 8
Therefore, eight students study mathematics and chemistry.
Learn more about set on:
https://brainly.com/question/9025420
#SPJ1
Jared had two numbers to multiply. They were written as 64⋅3.He thought that it would be easier to multiply them as 3⋅64.What property would he be using?
Answer:
He is using the commutative property of multiplication.
The fraction 3/5 fits into 2 1/5 more or less than 1? That means the quotient is more or less than 1?
The fraction 3/5 fits into 2 1/5 more than once. The quotient is more than one.
We are given two fractions. The first fraction is 3/5, which is a simple fraction. The second fraction is 2 1/5, which is a mixed fraction. We will first convert the mixed fraction into a simple fraction.
F = 2 1/5
F = (2*5 + 1)/5
F = 11/5
We need to find out if the quotient is more or less than one. So we will divide the second fraction by the first fraction. Let the quotient be represented by the variable "Q".
Q = (11/5)÷(3/5)
Q = (11/5)×(5/3)
Q = 11/3
Q = 3.667
We can see that the quotient is more than one. Hence, the fraction 3/5 fits into 2 1/5 more than once.
To learn more about fractions, visit :
https://brainly.com/question/10354322
#SPJ1
Answer:
the fraction 3/5 fits into 2 1/5 more than 1 time. That means the quotient is greater than.
Step-by-step explanation:
Out of 32 cards, Mookie guessed the color correctly 18 times. What would this be as a decimal? ((Type in 4 digits after the decimal))
Answer:
0.5625
Step-by-step explanation:
18/32=0.5625
hello am new here,so I want u guys to help me with the question and good workings and it is urgent.
using sine rule
In a triangle ABC the value of side a is 13.12 cm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know in a ΔABC, a/sinA = b/sinB = c/sinC.
GIven, In a ΔABC A = 29°, B = 36°, b = 15.8 cm.
∴ a/sinA = b/sinB.
a/sin(29°) = 15.8/sin(36°).
a/0.49 = 15.8/0.59.
a = (15.8×0.49)/0.59
a = 7.742/0.59.
a = 13.12.
learn more about the sine formula of triangles here :
https://brainly.com/question/1979489
#SPJ1
In the diagram below, GH is parallel to DE. If the length of DE is the same as the
length of GF, DF = 13, and GH = 5, find the length of GF. Figures are not
necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Using the properties of similar triangle and parallel lines we calculate the length of GF as √65 units.
It is given that GH is parallel to DE or GH || DE in the trapezium GHDE .
Therefore in the triangles ΔFDH and ΔFDE , we can say that
ΔFDH is similar to ΔFDE by angle angle angle axiom of similarity.
Now using the properties of similar triangles we can say that :
FG / DF = GH / DE
Now let us consider the length of GF be x.
Therefore DE = x
Now using the properties of similar triangles and substituting the values we get:
x / 13 = 5 / x
or, x² = 65
or, x = √65
Therefore the length of DE and GF is equal to √65.
To learn more about parallel lines visit:
https://brainly.com/question/29042593
#SPJ1
Write an equation in slope-intercept form for the line that passes through (9, 12) and is parallel to y=4
Answer:
y= 12
Step-by-step explanation:
Just change the y-value (b in y=mx+b)
bobby spent 40% of his allowance on art supplies last month, with two-thirds of this amount spent on paintbrushes alone. if his monthly allowance is $75, how much did bobby spend on paintbrushes last month?
Bobby spent $20 out of $75 of his monthly allowance on paintbrushes.
What is monthly allowance?
Giving someone money on a regular basis to help them pay for the things they need is known as giving them an allowance.
Main Body:
total monthly allowance = $75
Now Bobby spent 40% on his art supplies,
which means we need to calculate 40% of 75.
⇒(40/100)*75
⇒30
so Bobby spent $30 on art supplies.
now according to question,
Bobby spent 2/3 on paintbrushes
⇒2/3 of art supplies
⇒(2/3 )*30
⇒$20
Hence Bobby spent $20 on his paintbrushes.
Too know more about monthly allowance , visit;
https://brainly.com/question/28261654
#SPJ4