The solution to the equation 5x + 9y = 561 and 5x + 6y = 276 is x = -58.8, y = 95
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Given the equation:
5x + 9y = 561 (1)
Let us assume the second equation is:
5x + 6y = 276 (2)
To solve using elimination method, subtract equation 2 from 1:
3y = 285
y = 95
Put y = 95 in equation 1:
5x + 9(95) = 561
5x = -284
x = -58.8
The solution is x = -58.8, y = 95
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A farmer notes that in a field of horses and chickens there are 34 heads and 104 feet. How many of each animal are there
Answer: 18 horses and 16 chickens
Step-by-step explanation:
horses = h , chickens = c
h + c = 34
4h + 2c = 104, or simplified, 2h + c = 52
Now we just use systems of equations to solve. I will subtract the second equation from the first.
(2h + c = 52) -
(h + c = 34)
so simplified, our system becomes h = 18. Therefore, there are 18 horses. Now we can plug this value into h for any of the equations to get c, the amount of chickens.
18 + c = 34
c = 16.
Therefore, there are 18 horses and 16 chickens.
Giving 100 Points And Brainliest
Find the value of the trigonometric ratio.
Responses
13/5
12/5
12/13
5/12
Answer:
[tex]tan(A)=\frac{5}{12}[/tex]
[tex]\frac{5}{12}[/tex]
Step-by-step explanation:
The TAN function can be expressed as [tex]tan(x)=\frac{Opp}{Adj}[/tex].
The side opposite to angle A is 15
The side adjacent to angle A is 36.
Therefore
[tex]tan(A)=\frac{15}{36}[/tex]
We can simplify the fraction.
Factor 3 out of 15.
[tex]\frac{3(5)}{36}[/tex]
Factor 3 out of 36.
[tex]\frac{3(5)}{3(12)}[/tex]
Cancel the common factor of 3.
[tex]\frac{5}{12}[/tex]
Answer:
tan(A)=\frac{5}{12}tan(A)=
12
5
\frac{5}{12}
12
5
Step-by-step explanation:
The TAN function can be expressed as tan(x)=\frac{Opp}{Adj}tan(x)=
Adj
Opp
.
The side opposite to angle A is 15
The side adjacent to angle A is 36.
Therefore
tan(A)=\frac{15}{36}tan(A)=
36
15
We can simplify the fraction.
Factor 3 out of 15.
\frac{3(5)}{36}
36
3(5)
Factor 3 out of 36.
\frac{3(5)}{3(12)}
3(12)
3(5)
Cancel the common factor of 3.
\frac{5}{12}
12
5
Write an equation to represent the following: the product of the quantity
eight times a number x plus 4 and is equal to 17. Lesson 5-1
Answer:
8x+4=17
Step-by-step explanation:
4. A fancy dinner for your family cost $77.48 and a 15% tip was added on top of that, how much
was your total bill?
Answer:
89.102 dollar
Step-by-step explanation:
let x be the total amount of bill
77.48 ×15% =11.622
11.622 is the additional tip
x=original cost +additional tip
=77.48+11.622
=89.102 dollar
hello!! only the equations with stars by the numbers need to be done. you don’t have to do all 4 if you don’t have time but as much as u can do is so greatly appreciated!! i would need an image attached of a graph so i can fill it in! i will mark brainliest if done correctly xx “solve the equation by graphing. check your solution”
Answer:
3. x = - 2, 4. x = 1-----------------------------
Question 3Given equation:
x + 4 = - xIn order to solve it by graphing, plot two lines:
y = x + 4 and y = - xThe solution is the x-coordinate of the intersection of the lines:
x = - 2See the attached
Question 4Given equation:
-2x + 6 = 5x - 1Similar to the previous question, plot the lines and take the x-coordinate of the intersection as solution.
y = - 2x + 6 and y = 5x - 1The solution is x = 1.
See the attached.
A cookie factory uses 3 3/4 bags of flour in each batch of cookies. The factory used 7 1/2 bags of flour yesterday. How many batches of cookies did the factory make?
Answer:
To find out how many batches of cookies the factory made, we need to divide the total amount of flour used (7 1/2 bags) by the amount of flour used per batch (3 3/4 bags).
We can start by converting 7 1/2 bags of flour to a mixed number: 7 1/2 bags = 7 + 1/2 = 7.5 bags
Next, we can convert 3 3/4 bags of flour to a mixed number: 3 3/4 = 3 + 3/4 = 3.75 bags
Then, we can divide the total amount of flour used by the amount of flour used per batch:
7.5 bags / 3.75 bags/batch = 2 batches
Therefore, the factory made 2 batches of cookies yesterday
please answer and help
Answer:
The third option.
Step-by-step explanation:
Lets write the length as L and the width as W.
Given, L = W - 4
or L - W = - 4
Perimeter of a rectangle = 2( L + W)
44 = 2 (L + W)
L + W = 22
L - W = -4
2L = 18 (adding the two equations)
L = 9
W = 13
So, the answer is the third option.
Cheers
are the two triangles below similar? If so, write a similarity statement in state which similarity criteria can be used to prove it?
A. Similarity Statement
1. ABC DEF
2. ABC FDE
3. ABC EFD
4. The triangles are not similar
B. Criteria
1. AA
2. SAS
3. SSS
4. Not applicable, the triangles are not similar
Similarity is the mathematical property of triangles. Two triangles are called similar if they fulfil wither of the properties: Angle Angle, wherein two angles should be congruent; Side Angle Side, wherein two sides are similar to each other and the angles congruent to each other; and Side Side Side, wherein three sides are similar to each other in ratio.
The triangle ABC and triangle EDF are similar.
The first property is angle,
∠BAC = ∠EDF = 65°
The second property is also angle.
∠ABC = ∠DEF = 48° (∠DEF = 180 - 65 - 67)
Thus, the three angles are same or congruent.
The AA property of similarity makes the two triangles ABC and DEF similar. The option 1 is correct.
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how do you find the difference between the points shown? what is the difference between point A and point B
Answer:
Step-by-step explanation:
Sorry but there isn't a picture here
What is the most general form of a polynomial function of degree n that has real coefficients, and how do you determine the number of distinct roots of that polynomial function using the fundamental theorem of algebra and the factor theorem, while also taking into consideration any constraints or limitations imposed by the discriminant and the nature of the roots (real or complex)?
Answer:The most general form of a polynomial function of degree n that has real coefficients is:
f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0
where a_n, a_{n-1}, ..., a_1, a_0 are real numbers, and a_n is not equal to zero.
The number of distinct roots of a polynomial function of degree n can be determined using the fundamental theorem of algebra, which states that a polynomial function of degree n has exactly n roots, counting multiplicities. This means that a polynomial function of degree n can have n distinct roots, n-1 distinct roots, or any integer value in between, depending on the multiplicities of the roots.
Using the factor theorem, it is possible to determine the number of distinct roots of a polynomial function by factoring it into its irreducible factors. If the polynomial function is fully factored, the number of distinct roots is equal to the number of irreducible factors.
However, the nature of the roots (real or complex) and constraints imposed by the discriminant are also important to consider. The discriminant of a polynomial function is the value of the expression b^2-4ac, where a, b, and c are the coefficients of the polynomial function in the form f(x) = ax^2+bx+c. The discriminant determines the nature of the roots of the polynomial function. If the discriminant is positive, the roots are real and distinct. If the discriminant is zero, the roots are real and repeated. If the discriminant is negative, the roots are complex and non-real.
So, the most general form of a polynomial function of degree n that has real coefficients, can be determined by the form of the polynomial, the number of distinct roots by the fundamental theorem of algebra, by factoring the polynomial into its irreducible factors and the nature of the roots is determined by the discriminant.
Step-by-step explanation:
a train from london to bristol takes 30 km per hour and a train from bristol to london is 50 km per 1 hour when will the two trains meet up.
London to bristol is 100km
Answer:
In order to find when the two trains will meet up, we can use the concept of relative speed. The relative speed of two trains is the sum of their individual speeds.
In this case, the relative speed is 30 + 50 = 80km/h
Since we know that the distance between London and Bristol is 100km, we can divide the distance by the relative speed to find the time it takes for the two trains to meet up:
100km / 80km/h = 1.25 hours
So, the two trains will meet up in 1.25 hours
Answer:
1 hour 15 minutes
Step-by-step explanation:
Relative Speed
If the two objects are moving in the opposite direction at different speeds, relative speed is the sum of their two speeds:
[tex]v_1+v_2[/tex]Using the formula:
[tex]\boxed{\sf Time=\dfrac{Distance}{Speed}}[/tex]
Therefore:
[tex]t=\dfrac{d}{v_1+v_2}[/tex]
where:
v₁ is the first body’s speed.v₂ is the second body’s speed.d is the distance between the two bodies.t is the time when the two bodies meet.Given:
v₁ = 30 km/hv₂ = 50 km/hd = 100 kmSubstitute the given values into the formula to find the time at which the two trains meet:
[tex]\implies t=\dfrac{100}{30+50}=\dfrac{100}{80}=1.25\; \sf hours=1\; hour\;15\;mins[/tex]
Therefore, the two trains meet at 1 hour 15 minutes.
what is the answer to this equations
4(a+b)
= 4a + 4b
Answer:
[tex] \sf \: 4a + 4b [/tex]
Step-by-step explanation:
Given expression,
→ 4(a + b)
Let's simplify the expression,
→ 4(a + b)
→ 4(a) + 4(b)
→ (4 × a) + (4 × b)
→ 4a + 4b
Hence, the answer is 4a + 4b.
Grayson can spend a maximum of 3 hours,h, watching television on the weekend
Grayson can spend a maximum of 3 hours, h, watching television on the weekend, and is shown in the number line.
What is number line?Numbers on a straight line are represented graphically as a number line. For comparing and sorting numbers, it serves as a reference. Including all whole numbers and natural numbers, it can be used to represent any real number.
Just to refresh your memory, the natural number is the collection of all counting numbers, i.e. 1, 2, 3, 4, 5, 6, while the whole number is a set of numbers that includes both zero (0) and all counting numbers.
Compare numbers more easily by writing them on a number line. The integers in the above figure are smaller on the left than they are on the right, as can be seen.
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Grayson is only permitted to watch television for a total of three hours on the weekends. 8-10. 5-5, 5-6 7.5-6
How do you calculate time in an hour?[Time = Distance Speed] is the formula for calculating time. The time formula can be changed to [Distance = Speed Time] to compute distance. Find the vertex of the parabola given a generalised quadratic function. Find a, b, and c. By changing a and b into h=-b2a, you can determine h, the vertex's x-coordinate. By evaluating k=f(h)=f(b2a), you may determine k, the vertex's y-coordinate.
In order to get the vertex (h, k) of the given quadratic y = ax2 + bx + c, one must first compute h= b 2 a h=2ab 2a, and then one must evaluate y at h in order to determine k. The speed equation is speed=distance*time. According to the currently accepted definition of the kilogramme, it reads as follows: "The kilogramme is defined by considering the fixed numerical value of h to be 6.62607015 unit Js,"
The fact is [tex]$3 \geqslant h \geqslant 0$[/tex]
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Find the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.
There are 28 ways of choosing three points from the grid below, so that they form an isosceles right triangle.
What is an isosceles triangle?A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.
The grid figure is given in the attached image.
The given image displays seven triangles (counting the original 2).
There can be 7 x 4 = 28 isosceles right triangles,
since each has degree 4 rotational symmetry around the figure's center.
The complete figure is given in the image.
Therefore, there are 28 ways of choosing three points from the grid below.
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Determine if the graph represents is a function.
If so, determine if the function is one to one.
not function, not one-to-one
function, one-to-one
function, not one-to-one
not function, one-to-one
ASAP Which expression is equivalent to 1/3 b - 7?
Answer: Your answer is 1/3(b-21), aka the first answer slot
Step-by-step explanation: If we factor 1/3b-7, the common factor is 1/3. by this knowledge, we put 1/3(b-7/1/3), and 7/1/3 = 7x3 which is 21. So we simplify and get the answer
1/3(b-21)
Giving 100 Points
Question
Find the value of the trigonometric ratio.
Responses
454 fifths
545 fourths
434 thirds
35
Answer:
cos X = 3/5
Step-by-step explanation:
Cosine is a ratio. The side (leg) adjacent to Angle X is the side (leg) next to the angle. The hypotenuse is the longest side.
Cosine is the ratio of the Adjacent side /Hypotenuse.
In this image,
cos X = adj/hyp
cos X = 15/25
cos X = 3/5
cos X = 3/5
(Like the weird wording in the question:
3 fifths)
Ansley purchased 100 shares of a certain stock 6 years ago for $2545.30. The stock has a steady annual percentage rate of growth and is now worth $4152.57. What is the approximate annual growth rate of the stock?
1) 8.5%
2) 26.8%
3) 2.7%
4) 0.85%
Answer:
2
Step-by-step explanation:
To find the approximate annual growth rate of the stock, we can use the formula for compound annual growth rate (CAGR):
CAGR = (Ending value / Beginning value)^(1/n) - 1
Where n is the number of years.
In this case, the beginning value is $2545.30, the ending value is $4152.57 and the number of years is 6.
So, CAGR = (4152.57 / 2545.30)^(1/6) - 1
The CAGR is approximately 26.8% which is the answer 2.
A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as much in the lower-yielding account because it is less risky. His annual interest is $3080 dollars. How much did he invest at each rate?
Answer:
Step-by-step explanation:
Let x be the amount invested in the 6% account.
Since he invested twice as much in the lower-yielding account, the amount invested in the 10% account is 2x.
We know that the annual interest is $3080 dollars, and the interest is calculated on the invested amount at each rate.
The interest in the 6% account is (6/100) * x = 3/50 * x
The interest in the 10% account is (10/100) * 2x = 1/10 * 2x
The total annual interest is 3/50x + 1/102x = 3/50x + 1/5x = (3+1)/5x = 4/5x
Therefore, we can write the equation:
4/5*x = 3080
To find x, we can divide both sides by 4/5:
x = 3080*5/4
x = $2310
So, the man invested $2310 in the 6% account and $2310*2 = $4620 in the 10% account.
A printer has 14 rolls of newsprint in the warehouse. What fraction of this total will remain if four rolls are used?
what is the slope of this graph showing?
Answer: -4/5
Step-by-step explanation:
(0,2) and (4,-3) are two coordinates here.
Using the slope formula, i.e, m = (y₂ - y₁)/(x₂ - x₁) = 4/-5 = -4/5
39 oz to ____ lb ____ oz
Answer:
2.4375 pounds
We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. The numbers 222, 72, 45, and 810 and are all cozy. Also, the numbers 202 and 2772 are cozy.
How many 2-digit numbers are cozy?
How many 3-digit numbers are cozy?
The number of three digit number formed are-
Repetition allowed = 125
Repetition not allowed = 60
What is defined as the combination?A combination is an algebraic technique for determining the number of distinct arrangements in a set of items in which the sequence of the selection is irrelevant.
here, we have,
You can choose the items in either order in combinations. Permutations and combinations are often confused.
For the given question;
The three digit number is to be formed.
The digits are given as- 1,2,6,7,8
Case 1: Repetition allowed
The number of combination will be;
= 5×5×5
= 125
Thus, the number of three digit number formed with repetition is 125.
Case 2: Repetition not allowed
The number of combination will be;
= 5×4×3
= 60
Thus, the number of three digit number formed with without repetition is 125.
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The circumference of the hub cap of a tire is 78.06 centimeters. Find the area of this hub cap. Use 3.14 for . π Use pencil and paper. If the circumference of the hub cap were smaller, explain how this would change the area of the hub cap.
Answer: 485.14 cm^2 (rounded)
Step-by-step explanation: Pi * Diameter = 78.06 -> 78.06/ 3.14 or Pi = radius or 12.429. That squared is 154.5. Then multiply it by Pi to get the answer.
Explain how you could use mental math to find the following sum. Then find the sum. Support your answer with a model
The mental math for the fraction is shown below.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Model: 1 1/4 + 2 1/3 + 3 2/3 + 4 1/2 + 5 1/2 + 6 3/4
Now, if we use mental math then we can add the whole number first.
1 + 2 + 3 + 4 + 5 + 6 = 21
Now, add the fraction with same denominator
1/3 + 2/3 = 3/3 = 1
1/2 + 1/2 = 1
1/4 + 3/4 = 4/4 = 1
Finally add all of them
21 + 1+ 1 +1= 24.
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Which statement about a histogram is true?
Group of answer choices
A peak is a bar that is higher than the other bars around it.
A cluster means the frequency is zero.
A mirror image of the left and right side of a histogram means there is a peak in the middle.
If the graph has a cluster, the data is evenly distributed.
The true statement about a histogram is A. A peak is a higher bar than the other bars around it.
What is a histogram?A histogram is a pictorial representation of data using vertical bars of equal width but different heights with no spaces between the bars.
Histograms are graphical representations of the frequency of numerical data using rectangular bars.
The height of the histogram represents the frequency of the variable of interest.
A Histogram as a graph shows the distribution frequency of continuous data, making it easier to interpret.
Histograms summarize and provide a visual interpretation and comparison of data.
Thus, the highest bar in height represents the peak; therefore, Option A is correct since Options B, C, and D do not refer specifically to a histogram.
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what is the slope of y= 4x-5
Answer:
it is 4
Step-by-step explanation:
the slope is always the number before x and so since 4 is before x then 4 is the answer
Babies are illogical .nobody is despised who can manage a crocodile . Illogical person are despised identify one valid conclusion.
A.) if you are a baby,then you are despised.
B.) if you are despised, then you are a baby
C.) if you are not baby , then you are not despised
D.) if you are logical , then you are a baby
What the correct answer?
The obvious conclusion from this question is that. C. if you are not a baby, then you are not despised.
What is logic?
Logic can be defined as the study of rational thinking. It contains both formal and informal logic. Deductively sound inferences or logical truths are studied in formal logic. It is a formal science that examines the topic-neutral ways in which conclusions flow from premises. As opposed to informal logic, which is connected to argumentation theory, critical thinking, and informal fallacies, formal logic is a branch of logic.
Philosophy, mathematics, computer science, and linguistics are just a few of the disciplines where logic is crucial. A set of premises and a conclusion make up an argument, which is the subject of logic. Arguments can be proven right or wrong. If the premises of an argument support the conclusion, then it is valid.
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si (x+2)=4 cual es el resultado de 3(x+2)^2=4
The result of the expression 3(x + 2)² - 4 is equivalent to 44.
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given is the equation as -
(x + 2) = 4
We have to find the result of -
3(x + 2)² = 4
It is given that -
(x + 2) = 4
So, we can write -
3 x 4 x 4 = 4
48 - 4
44
Therefore, the result of the expression 3(x + 2)² - 4 is equivalent to 44.
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{Question in english -
If (x+2)=4 what is the result of 3(x+2)^2=4}
Thhe study of choices people make to fulfill their unlimited needs and wants even though there are limited resources.
Group of answer choices
Economics
Scarcity
Choices
Opportunity Cost
The study of choices people make to fulfill their unlimited needs and want even though there are limited resources is called Economics. Thus option A is correct.
What are resources?Resources can be defined as the means through which the material is provided to people. This will be to know that the resources are properly allocated.
An economy is a region where products and services are produced, distributed, traded, and consumed. a social domain that places an emphasis on production-related practices, discourses, and material expressions. The factors that affect production, such as land, cash, labor, and natural facilities, are governed by economic structures.
Therefore, option A is the correct option.
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