There are 6 goats and 17 ducks present in the farmhouse
How to calculate the number of goats and ducks ?Let x represent the number of goats
Let y represent the number of ducks
x + y= 23....equation1
Goats have 4 legs and ducks have 2 legs
4x + 2y= 58.......equation 2
From equation 1
x + y= 23
x= 23-y
Substitute 23-y for x in equation 2
4(23-y) + 2y = 58
92- 4y + 2y= 58
92-2y= 58
-2y= 58-92
-2y= -34
y- 34/2
y= 17
Substitute 17 for y in equation 1
x + y= 23
x + 17= 23
x= 23-17
x= 6
Hence there are 6 goats and 17 ducks in the farmhouse shelter
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Answer to the graph ok
Answer:
(4,-3)
Step-by-step explanation:
The point at which the line’s cross is the solution
1) In the given figure, name (a) the vertex opposite A to side AB (b) the angle opposite to side AC (c) the angle made by the sides CB and CA.
In this case, the arms of $angle ABC$ are represented by AB and AC, which are two rays that unite to make an angle. The vertex of angle $angle ABC$ is B in this case. It is the common terminal point where rays meet to form an angle.
What is vertex in angle ABC?The vertex and arm of the provided ABC must be found in this question. Vertex information is required for this puzzle. Angles are formed when two rays share a terminal. The vertex is the term for the shared endpoint. Alternatively, vertex refers to the shared terminal point where two rays converge to form an angle. Likewise, we must understand what an angle's arm is. An angle's arm is made up of the two rays that unite to make it. Here, an angle of ABC was provided. Specifically, we must identify the angle's vertex and arm.The arms of the ABC formula are represented by AB and AC, two rays that unite to make an angle.The vertex of ABC is the common terminal point where rays converge to form an angle. In this case, B is the vertex.AB and AC make up the arms of ABC, and B serves as the vertex.To Learn more About vertex of angle Refer To:
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1/4 cup are in 4 cups
The possible values for the number of hours lifeguarding, is 5,4 hours and the number of hours tutoring, is 5,6 hours that Brianna inequality equation can work in a given week.
What does a mathematical inequality equation mean?In Algebra, an inequality is a mathematical statement that uses the inequality symbol to depict the relationship between two expressions. An inequality sign has non-equal expressions on both sides.
Use these steps to resolve an inequality: Eliminate fractions in Step 1 by multiplying all terms by the total fractions' lowest common denominator. On both sides of the inequality, combine like phrases to simplify in Step 2. To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts.
16h + 11t ≥ 130
16*5=80, 16*4=64
11*5=55, 11*6=66
80x+55y>130
64x+66y>130
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i don’t understand:(
The measure of the exterior angle is 70° .
What is the measure of the exterior angle ?Exterior angle = Sum of two opposite interior angles of a triangle.
(2x- 8)° = x° + 31°
2x- x = 31 +8
x = 39
So, Substituting the value of x in the exterior angle.
(2x- 8)° = 78 - 8
= 70°
What is the exterior angle of a triangle?One side of a triangle can be extended to form an external angle. An exterior angle is the angle formed by the extended side and the adjacent side. According to the external angle theorem, when a triangle's side is extended, the resulting exterior angle is equal to the sum of the measurements of the triangle's two opposed internal angles. A triangle's unknown unknown angle can be measured using the theorem.To use the theorem, we must first determine the triangle's exterior angle and then its two remote interior angles. Exterior angles are those created between a polygon's side and its extended neighbouring side.To learn more about exterior angle , refer:
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Question 6(Multiple Choice Worth 2 points)
(Linear Relationships LC)
Which of the following tables represents a linear relationship that is also proportional?
x y
0 0
4 2
8 4
x y
0 1
2 3
4 5
x y
0 2
3 5
6 8
x y
0 3
6 5
12 7
Table 1 is the correct answer.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given: Table 1
x y
0 0
4 2
8 4
Clearly here x=2y which is proportional equation with 2 being the constant with x varying directly with the value of y
Hence, Table 1 is the correct answer.
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in order to graph your solutions solve for the variable be sure to show your work
Variable x isb5 is the answer to the equation 6 is 3x - 9 in the given situation.
The equation is what?A mathematical statement is considered to be an equation if it contains at least two terms with equal amounts of variables or integers.
We can start by focusing on the variable on one side of equation 6 = 3x - 9 in order to find a solution. We may accomplish this by adding 9 to both sides, giving us:
6 + 9 = 3x
Simply put, this means:
15 = 3x
The next step is to divide the equation's two sides by 3, which will yield the answer to the question "what is x?"
15/3 = 3x/3
We obtain 5 = x by simplifying.
Consequently, x = 5 is the answer to the variable.
The complete question is,
Locate the answer to the variable in the following equation. Use entire sentences to describe the problem-solving procedure you used to come up with a solution, and be sure to present all of your efforts. Include two words from the word bank at the very least.
6 = 3 x - 9.
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Factorise (pls show steps)
12y^2 - 20y - 8
Answer:
12y( y-1 ) - 8( y+1 )
Step-by-step explanation:
12y^2-20y-8 = (12y^2- 12y) - (8y+8) = 12y( y-1 ) - 8( y+1 )
Select the expressions that have a
quotient of 9.
1.35 ÷ 1.5
1.35 0.15
13.5 ÷ 1.5
13.5+ 0.15
Answer:
1.35/0.15
13.5/1.5
Step-by-step explanation:
We know the first and last ones are incorrect. The last is incorrect because it uses addition when the question is asking for the quotient. The first is incorrect because 1.35/1.5 = 0.9. The quotient (or answer) for the rest all equal 9.
1.35/0.15 = 9
13.5/1.5 = 9
Students in Mrs.Whites class took their Chapter 1 math test on Monday
Answer:
Step-by-step explanation:
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A college student plans to use a credit card to cover the cost of purchasing a $3,200 campus meal plan. If the credit card has annual interest rate of 12.99% compounded continuously and the student plans to pay off the loan in 15 months, how much interest will be owed? $739.25 $688.41 $588.69 $564.16
If a college student plans to use a credit card to cover the cost of purchasing a $3,200 campus meal plan. The amount of interest that will be owed is: D. $564.16.
How to find the interest amount?Using this formula to
I= Pe^rt - P
Where:
I = Interest amount = ?
P = Principal = $3,200
e = Exponential
r = Rate = 12.99% or 0.1299
T =Time = 15 months/12 = 1.25
Let plug in the formula
Interest amount = ( $3,200e^0.1299× 1.25) - $3200
Interest amount = ( $3,200e^0.162375) - $3,200
Interest amount = $3,764.16 -$3,200
Interest amount = $564.16
Therefore we can conclude that the correct option is D.
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Given f(x) = 2x - 3, find f(3).
Answer:
f(3) = 3
Step-by-step explanation:
f(x) = 2x - 3
f(3) = 2(3) - 3
f(3) = 6 - 3
f(3) = 3
Use a system of equations to solve the following problem.
The sum of three integers is 45. The sum of the first and second integers exceeds the third by 69. The third integer is 65 less than the first. Find the three integers.
Answer:
53, 4, -12
Step-by-step explanation:
Let the first, second, and third integers be a, b, and c, respectively.
a + b + c = 45
a + b = c + 69
c = a - 65
Using the third equation, substitute the value of c, a - 65, for c in the first two equations.
a + b + a - 65 = 45
a + b = a - 65 + 69
2a + b = 110
b = 4
2a + 4 = 110
2a = 106
a = 53
c = a - 65
c = 53 - 65
c = -12
a = 53; b = 4; c = -12
Answer: 53, 4, -12
Finish the table that represents the relation.
{(-2, 3) , (2, -1) . (3, 3) , (5, -4) , (9, 12)}
The table that represents the relation are out put 3 input 3, input 2 out put -1, input 5 out put -4.
How can you locate a table that illustrates a function?Find out if a table of input and output values is a representation of a function. The input and output values should be noted.
Verify that every input value is matched with just one output value. Consequently, the table is a function in that case.
A relation is a rule that links the constituents of one set to those of another. Relationships can be visualized using graphs, ordered pairs, tables of values, equations, or mapping diagrams. Every input in a relation results in one or more outputs.
According to question:-
out put 3 input 3
input 2 out put -1
input 5 out put -4.
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van someone help w this paper
Assume that
x is the total number of hours that you and your pals skate at Sam's or Brad's Skate Park, and y is the cost of skating as a whole.Sam's Skate Park charges $3 to enter the facility, $1 for each hour of skating, $1 for a total of x hours, and y=(3+x).Brad's Skate Park costs $5 to enter, $0.50 per hour of skating, then $0.5 per hour for a total of y=(5+0.5x).First gap: y=(3+x)
Second gap: y=(5 + 0.5 x)
x represents the total number of hours you and your pals skate at Sam's or Brad's Skate Park, and y represents the cost of skating. Compare the two expressions:3+x=5+0.5x,
x-0.5x=5-3,
0.5x=2,
5x=20,x=4.
When skating for 4 hours, the total costs in the two parks are equal.The cost for three hours at Sam's skate park is $(3+3)=$6, whereas the cost at Brad's skate park is $(5+30.5)=$6.5. The best deal is at Sam's Skate Park where admission is $6–$6.5.To know more about Find the Value for X and Y refer to :
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Please help I don’t understand!
Therefore , we can conclude from answering the given question of equation that dy/dx =2t² = > dy/dxat (5,3) = -2 is the solution to the following problem.
Describe equation.An equation is an mathematical formula that joins two statements with the equivalent symbol = to express equality. In algebra, an equation is defined as a formula that asserts that two formulae are equivalent. For instance, an equal sign separates the components three times + 5 and 14 in the equations 3x + 5 = 14. In mathematical formulas, especially equations, the equal sign is a necessary varaibles. Equations frequently make use of algebra. When we don't have a precise quantity to compute in math, algebra is used.
Here,
In this instance,
x=5 + In(t)
=>y=t² + 2
=> dx/dt=1/t
=>dy/dt=2t
=>dy/dx=2t²
=> dy/dx at (5,3) = -2
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oes the name describe the quadrilateral? Choose yes or no.
A quadrilateral has two pairs of opposite sides and no right angles. The opposite sides are parallel and equal in length, but adjacent sides are not the same length.
parallelogram
Choose...
trapezoid
Choose...
rhombus
Choose...
rectangle
Choose...
Answer:
1) parallelogram: Yes
2) trapezoid: No
3) rhombus: No
4) rectangle: No
Step-by-step explanation:
1) A parallelogram has two pairs of opposite sides and no right angles. The opposite sides are parallel and equal in length, but the adjacent sides are not the same length.
2) A trapezoid's opposite sides are parallel but not equal.
3) All sides of a rhombus are equal.
4) The four sides of a rectangle are right-angled.
The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling. Weight (lbs.) Rolling Distance (m.) 59 26 84 43 97 48 56 20 103 59 87 44 88 48 92 46 53 28 66 32 71 39 100 49 Can it be concluded at a 0.05 level of significance that there is a linear correlation between the two variables?
It can be concluded that there is a significant linear relationship between weight and rolling distance at a 0.05 level of significance.
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Weight (lbs.) Rolling Distance (m.)
59 26
84 43
97 48
56 20
103 59
87 44
88 48
92 46
53 28
66 32
71 39
100 49
Using a graphing calculator, we have the following summary:
t = 2.739
df = 10
p-value = 0.0208
The p value is less than 0.5
So, we accept the alternative hypothesis
Hence, there is a significant relationship
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Consider the function f(x) = x ^ x + 5 with domain x >= 0 , and its Inverse , f ^ - 1 * (x) = sqrt(x) - 5 What are the domain and range of f(x) and f ^ - 1 * (x) Express the domain and range as Inequalities
Regardless of the sign of the inequality, the domain and range of a linear inequality are always all real numbers.
How do you find the domain of an inequality?Regardless of the inequality's sign, the domain and range of a linear inequality always include all real numbers. The vertex will determine the scope of the absolute value inequality. Intervals of the x values derived from zeros will decide the domain and range for polynomial inequalities.
The domain of the function is all values of x that are larger than or equal to zero, and we would write Read as an inequality if it were a mathematical statement. Inequalities is a good place to learn more about them. The identical function has a domain of in 'interval notation'. This is used to define the range of numbers from 0 to positive infinity.
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John has 37 marbles for his collection. He gives 17 marbles to his friend Zach. How many marbles does he have left?
Answer:
20
I wish you good luck on your assignments.
The model represents a division equation.
Determine whether each statement is true or fa
Select True or False for each statement.
Please double check my work!
50 points!!!
The above statements are
A) True
B) True
C) False
D) False
What is the division equation?
The division equation is a mathematical operation that represents the process of determining the number of times one number, called the divisor, can be subtracted from another number, called the dividend, without going negative.
A) The whole bar represents 4/5 -> TRUE
B) The model is divided into 1/8 equal parts -> TRUE
C) The model is divided into parts each worth 1/10. -> FALSE
D) The model represents the division equation 4/5 ÷ 1/10= 8 -> FALSE.
Hence, the above statements are
A) True
B) True
C) False
D) False
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Mr. Luthi is taking his 30 passing students on a field trip to the aquatic center. They will all get a ticket to
enter and swim as well as a serving of pizza and ice cream that costs $3 per student. Ms. Byer's is taking her
12 passing students on a field trip to the museum. Their tickets cost twice as much and they all get a
souvenir t-shirt for $10. Ms. Byers and Mr. Luthi paid the same amount for their field trips. How much did
tickets to each field trip cost?
The total trip cost approx $140
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Mr. Luthi took 30 passing students and they each get a pizza and a ice cream. let the cost of the ticket be t then we have
Cost = 30t+90
Similarly for Mr. Byers students the total cost is=12t+120
Now as per question they paid the same amount for the field trips '
Thus we have, 30t+90= 12t+120
18t=30
t=$1.66
Thus 12t+120= 140(approx)
Hence, The total trip cost approx $140
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Let's be any real number such that 4 < √ s <9. Which of the following is a possible value of s?
A. 2.5
B. 7.6
C. 12.7
D. 39.3
E. 82.4
The possible real number for the variable s is 39.3 (letter D).
Power and Square RootsIt is common in math solutions, you multiply a number by itself. See the examples below.
2 x 2 =4
3 x 3 = 9
4 x 4 = 16
In math, you can use the power to represent a multiply a number by itself using the operation power. Let's consider the previous example for a better understanding.
2 x 2 = 2²
3 x 3 = 3²
4 x 4 = 4²
Therefore, the power represents the number of times the numeral repeats in a product. It is important to know that the inverse operation of power is the root. Thus,
2²=4 and [tex]\sqrt{4}[/tex]= 2
The question asks you the possible value of s.
If [tex]4 < \sqrt{s}[/tex], you can apply power operation on both sides, for eliminating the root.
[tex](4)^2 < (\sqrt{s})^2\\ \\ 16 < s[/tex]
Another inequality is [tex]\sqrt{s} < 9[/tex]. Then, one more time you will apply power operation on both sides, for eliminating the root.
[tex](\sqrt{s})^2 < (9)^2 \\ \\ s < 81[/tex]
Combining the intervals you have: 16< s< 81. Now, let's analyze the given options.
A. 2.5 - It is not contained in the given range 16< s< 81.
B. 7.6 - It is not contained in the given range 16< s< 81.
C. 12.7 - It is not contained in the given range 16< s< 81.
D. 39.3 - It is contained in the given range 16< s< 81.
E. 82.4 - It is not contained in the given range 16< s< 81.
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An odd integer is represented by x. Which expression represents the next consecutive odd integer?
The expression which represent consecutive odd integer is 2x+1.
What is odd integer?
Any integer that cannot be divided by two is referred to as an odd number. In other words, integers that take the form 2k+1, where k , are referred to be odd numbers. Integers or sets of integers on a number line can be either odd or even, it should be noted.
Here let us take the odd integer as x.
Now the expression which expression consecutive odd integer is,
=> 2x+1 .
Here x is a real number.
Hence the expression which represent the next consecutive odd integer is 2x+1.
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The expression which represent consecutive odd integer is 2x+1.
What is odd integer?Any integer that cannot be divided by two is referred to as an odd number. In other words, integers that take the form 2k+1, where k , are referred to be odd numbers. Integers or sets of integers on a number line can be either odd or even, it should be noted.
Here let us take the odd integer as x.
Now the expression which expression consecutive odd integer is,
=> 2x+1 .
Here x is a real number.
Hence the expression which represent the next consecutive odd integer is 2x+1.
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Confusing question:
Please help quickly!
The value of angle x based on the information given is 45°.
How to determine the value of angle x?Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life
From the image ∠BEC = 160°, ∠FED = 115° and ∠AEF = x°
∠AEC = 180 - 160 = 20° (sum of angles on a straight line)
∠DEB = ∠AEC (vertically opposite angles)
∠DEB = 20°
It should be noted that vertically opposite angles are equal just as denoted above.
x = 180 - ∠DEB - ∠FED (sum of angles on a straight line)
It should be noted that the sum of angles that are on a straight line is 180°.
x = 180 - 20 - 115
x = 45°
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according to the u.s. census bureau, 23.5% of people in the united states are under the age of 18. in a random sample of 250 residents of a small town in ohio, 28% of the sample was under 18. which one of the following statements is true?
The percentage of people under 18 in the sample of 250 people from Ohio is higher than the percentage of people under 18 in the United States.
This can be demonstrated mathematically using the following formula: (28/250)*100 = 11.2%. This is higher than the US percentage of 23.5%, which indicates that the sample of 250 people from Ohio had a higher proportion of people under 18 than the US population as a whole. To calculate this, we can use the formula to find the difference between the two percentages: (28% - 23.5%) = 4.5%. This means that the small town in Ohio has a higher percentage of people under 18 than the national average. Therefore, it is true that the percentage of people under 18 in the small town in Ohio is higher than the national average.
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Solve the system of equations by graphing.
y = -2
y = -3
2
x + 4
The system of graphs is a very unique concept which helps to understand various concepts in a visual way.
How does this occur?
The two lines intersect at (-3, -4), which is the system of equations' solution.
Using the slope and y-intercept, graph an equation as follows:The equation y = mx + b's y-intercept can be found.Determine the y-intercept. The purpose will be (0, b).The slope=m of the equation y = mx + b can be found.Run from the slope while taking a single step using the rise.Your line should join those two spots.This is how the equation can be solved-
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What is the probability that a test correctly rejects a false null hypothesis called? Choose the correct answer below. A. P-value B. power of the test C. Type II error D. significance level
The correct answer is B. power of the test
The probability that a test correctly rejects a false null hypothesis is referred to as the power of the test. It is a statistical measure that helps us to determine the effectiveness of a test in detecting a real difference or effect when it exists. The power of the test is generally represented by the Greek letter beta (β) and is calculated as 1-β.
A test with a high power value is more likely to correctly reject a false null hypothesis, which means it is better at detecting the real difference or effect when it exists. On the other hand, a test with a low power is more likely to fail to reject a false null hypothesis, which means it is not as effective in detecting the real difference or effect. The p-value and significance level are also statistical measures used in hypothesis testing, but they are not directly related to the power of the test.
P-value refers to the probability of observing a test statistic as extreme or more extreme as the one observed, given that the null hypothesis is true. Significance level refers to the threshold of p-value beyond which the null hypothesis will be rejected.
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Find an angle θ conterminal −464 ° , where 0 degree ≤θ<360 °
Thank you!
The coterminal angles of -464° are -104° and -824°.
What are coterminal angles?Coterminal angles are the angles that have the same initial side and terminal sides.
To find the coterminal angle we add or subtract 360° from the given angle.
We have,
Angle = -464°
The coterminal angles of -464°.
(-464 + 360)° and (-464 - 360)°
Now,
(-464 + 360)° = -104°
(-464 - 360)° = 824°
Thus,
The coterminal angles are -104° and -824°.
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The definition of the absolute value of a number is its magnitude, or distance, from zero. How do these two definitions connect?
The way that the definitions of the absolute value of a number, connect is that the absolute value of a number is the positive representation of the number's distance from zero.
What is absolute value ?The absolute value of a number is the numerical value of a real number without regard to its sign. In other words, the absolute value of a number is the number's distance from zero on the number line. The absolute value of a number is always positive or zero, and is written as the number inside of absolute value notation, which is two vertical lines on either side of the number, like so: |number|. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.
The distance from zero is the same as the magnitude of a number, and the absolute value of a number is a non-negative representation of its magnitude. So, in other words, the absolute value of a number is its distance from zero on the number line. The two definitions are connected because the absolute value of a number is a positive representation of its distance from zero.
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Students in jakes class were numbered in order from 1 to 24 jake was asked to choose classmates numbered with multiples of 5 to be in his group which number could be the number of a classmate in his group
Answer:
the possible classmates numbered with multiples of 5 that Jake can choose are 5,10,15,20.
Step-by-step explanation:
Multiples of 5 are numbers that are obtained by multiplying 5 by any whole number. So, to find the classmates numbered with multiples of 5, we can start by multiplying 5 by 1, then by 2, 3, and so on. The first few multiples of 5 are 5, 10, 15, 20, 25 and so on. Since the students are numbered from 1 to 24, only students whose numbers are less than or equal to 24 can be chosen.
So the possible classmates numbered with multiples of 5 that Jake can choose are 5,10,15,20.