Answers
Correct option is A, (1,2) is the correct option for the given system of equations.
System of Equation -simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system).
The number of equations must match the number of unknowns for a system to have a singular solution.
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
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Related Questions
Interest is compounded semianually. Find the amount in the account after the given time. Principal Rate of Interest Time $2000 6% 3 years The amount in the account is $? (Round to the nearest cent)
Answers
Answer:
$2837.04
Step-by-step explanation:
semi-annually = every 6 month
p=2000
i=6%
t=3 years = 6 periods
compound 6 times in 3years = (1+6%)^6 =1.418519
multiply principal of $2000 = 2837.04
The play area in a local park ha the dimenion hown at the right. What i the area of the park? 25 m 24 m 30 m What i the bae of the triangle? What i the height of the triangle? PLEASE HELP
Answers
The area of parks is 360 m² , base and height are respectively 30m and 24 m.
Given a triangle shaped park with sides 25m, 24m and 30 m.
The total area that is bounded by a triangle’s three sides is referred to as the triangle’s area.
We know that area of triangle = ½ * base * height
Clearly show that base is 30m and height is 24 m.
So, area of triangle = ½ * 30 * 24 = 720/2 = 360 m²
Therefore, area of triangle shaped park is 360m².
Base and height are respectively 30m and 24m.
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10)
2(34 + 12) > 50
This inequality contains a variable, b. Choose ALL numbers that make this inequality true.
A)
16
B)
18
0
19
ELIM
D)
20
E)
22
11)
Which factorization is equivalent to this expression?
Answers
For the inequality "2(34 + 12) > 5b" that contain a variable "b" , then the numbers that make this inequality true are (a) 16 , (b) 18 .
The inequality containing the variable "b" is ⇒ 2(34 + 12) > 5b ;
simplifying the inequality ,
we have ;
⇒ 2×(46) > 5b ;
⇒ 92 > 5b ;
(a) Substituting value of b = 16 ,
we get ; 92 > 5×16
⇒ 92 > 80 , TRUE .
(b) Substituting value of b = 18 ,
we get ; 92 > 5×18
⇒ 92 > 90 , TRUE .
(c) Substituting value of b = 19 ,
we get ; 92 > 5×19
⇒ 92 > 95 , FALSE .
(d) Substituting value of b = 20 ,
we get ; 92 > 5×20
⇒ 92 > 100 , FALSE .
Therefore , the inequality is TRUE for two values of b that are (a) 16 , (b) 18.
The given question is incomplete , the complete question is
This inequality 2(34 + 12) > 5b ; contains a variable "b". Choose ALL numbers that make this inequality true.
(a) 16
(b) 18
(c) 19
(d) 20
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Given f (x)=9-14/x, find all c in the interval [2, 7] that satisfy the Mean Value Theorem
Answers
The value of c is √14 in the interval [2, 7], which satisfies the Mean Value Theorem.
By definition, the mean value theorem is
f'(c) = [f(b) - f(a)]/b - a
So, in this case, we know that a = 2 and b = 7.
Now, we need to find f(2) and f(7) by replacing those values with the given function
f(x) = 9 - 14/x
f(7) = 9 - 14/7 = 9 - 2 = 7
So, f(b) = f(7) = 7.
f(x) = 9 - 14/x
f(2) = 9 - 14/2 = 9 - 7 = 2
So, f(a) = f(2) = 2
Then, we replace all values,
f'(c) = [f(b) - f(a)]/b - a
= (7 - 2)/(7 - 2)
= 5/5
= 1
Now, calculate the derivative of the function, which has to be equal to 1,
f(x) = = 9 - 14/x
f'(x) = 14/x² = 1
Now, we solve the equation to calculate the value of c,
14/x² = 1
x² = 14
x = √14
Therefore, c = √14 is the value inside the given interval that satisfies the mean value theorem.
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how many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3, and 4? repetition of digits is allowed.
Answers
The integers greater than 999 but not greater than 4000 is 375.
Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers. The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.
The smallest number in the series is 1000, a4-digit number.
The largest number in the series is 4000, a4-digit number
The left most digits (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3×5×5×5 or 375 numbers from 1000 to 3999.
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A ski resort charges $14 for snowshoe rental, plus an additional dollar per hour. Let h represent the duration of a rental in hours and c represent the total cost of the rental. Complete the equation that represents the relationship between h and c.
Answers
c=14+xh is the equation that represents the relationship between h and c.
What is Expression?An expression is combination of variables, numbers and operators.
Given that ski resort charges $14 for snowshoe rental, plus an additional dollar per hour.
Let h represent the duration of a rental in hours and c represent the total cost of the rental.
We have to find the relationship between h and c.
c=14+xh
Here x represents the dollar.
Hence, c=14+xh is the equation that represents the relationship between h and c.
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Which of the following statements is true?
Answers
C
Step-by-step explanation:
c,c is the answer i think so
6. Which measure is equivalent to 660 feet?
7800 inches
mile
330 yards
1980 yards
Answers
=> Convert feet into yards.
660 feet = 220 yards.
=> Convert feet into inches.
660 feet = 7920 inches.
Now, According to the question:
=> Convert feet into inches.
660 feet = 7920 inches
Formula: multiply the value in feet by the conversion factor '12'.
So, 660 feet = 660 × 12 = 7920 inches.
=> Convert feet into yards.
660 feet = 220 yards
Formula: divide the value in feet by 3 because 1 yard equals 3 feet.
So, 660 feet = 660/3
660 feet = 220 yards.
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When filled to the brim, a swimming pool can hold 9.745 cubic yards of water. Calculate the width of the swimming pool if it has a length of 3 yards and a height of 2 yards.
Answers
The width of the swimming pool is 1.624yards.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Here, we have,
a swimming pool can hold 9.745 cubic yards of water.
i.e. V = 9.745
it has a length of 3 yards and a height of 2 yards.
i.e. l= 3
h=2
so, width = w = V/(l*h)
i.e. w = 1.624
Hence, the width of the swimming pool is 1.624yards.
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you know there are 2 boys and an unknown number of girls in a nursery at a hospital. then a woman gives birth a baby, but you dont know its gender, and it is placed in the nursery. then a nurse comes in a picks up a baby and it is a boy. given that the nurse picks up a boy, what is the probability that the woman gave birth to a boy?
Answers
The probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.
There are 2 boys initially and an unknown number of girls in the nursery, so there were a total of 2 + x babies in the nursery, where x is the number of girls.
Since we know that one of those babies is a boy, there are a total of 2 + x - 1 = 1 + x babies left in the nursery.
So the probability of the nurse picking up a boy, given that the woman gave birth to a boy, is 1/(1+x).
P(boy | picked up boy) = P(picked up boy | boy) * P(boy) / P(picked up boy)
= (1/(1+x)) * 1/2 / (1/(1+x) * 1/2 + x/(1+x) * 1/2)
= 1/3
So the probability that the woman gave birth to a boy, given that the nurse picked up a boy, is 1/3.
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X+3y=14 and 2x-3y=-8
Answers
To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables, such as x or y, by adding or subtracting the equations.
First we can eliminate the y variable by adding the two equations together:
X + 3y = 14
2x - 3y = -8
3x = 6
Dividing both sides by 3:
x = 2
Now we have the value of x, we can substitute it back into one of the original equations:
X+3y=14
2 + 3y = 14
Subtracting 2 from both sides:
3y = 12
Dividing both sides by 3:
y = 4
So the solution of the system of equations is (x,y) = (2,4)
To check the solution, we can substitute the values back into the original equations:
x + 3y = 14
2 + 3(4) = 14
2 + 12 = 14
14 = 14
and
2x - 3y = -8
2(2) - 3(4) = -8
4 - 12 = -8
-8 = -8
As the equation holds true, the solution (2,4) is correct.
Solve and classify the given system of linear equations. p=5(q+2) p=q-3
Answers
Answer:
q= -3.25 and p= -6.25
Step-by-step explanation:
p=5q+10. p=q-3
p-5q=10. p-q=-3 subtract the two equations
-4q=13 q= -3.25 and p= -6.25
4. A rectangle is 22 inches long and 10 inches wide. What is the length of the diagonal of the rectangle (the line that
goes across it from one corner to the next)?
Answers
The length of the diagonal of the rectangle is 24cm.
The diagonal of the rectangle equals the square root of the width squared plus the height squared.
The width of the rectangle is indicated by the letter “w” and the length of the rectangle is indicated by "l".So, the diagonal of a rectangle formula is expressed as d = (l² + w²),
According to the question,
A rectangle is 22 inches long and 10 inches wide.
To observe the diagonal we use the Pythagorean Theorem:
Let, x = hypotenuse
22² + 10² = x²
⇒484 +100 =x²
⇒x = 24.14 =24
So, the length of the diagonal of the rectangle is 24cm.
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Solve the following linear equations.
1. y + y+1 + y+2 = 90
2. 5(m+4)=-20
3. 3x-8=2x+2
Answers
Answer:
1. y=29
2. m= -8
3. x=10
Step-by-step explanation:
1. Add the numbers
y+y+1+y+2=90
y+y+3+y=90
combine like terms
3y+3=90
Subtract 3 from both sides
3y+3-3+90-3
3y=87
Divide both sides by the same factor
3y/3 = 87/3
y=29
2. Distribute
5(m+4)=-20
5m+20=-20
Subtract 20 from both sides
5m+20=-20
5m+20-20+-20-20
Simplify
5m=-40
Divide both sides by the same factor
5m/5 = -40/5
m= -8
3. Add 8 to both sides
3x-8=2x+2
3x-8+8+2x+2+8
Simplify
3x=2x+10
Subtract 2x from both sides
3x=2x+10
3x-2x+2x+10-2x
x=10
what is the distance between (-6 5) and (-6 -3.5)
Answers
The distance between (-6 5) and (-6 -3.5) is 14.71 units
How to find length of the lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (-6, 5) and (-6, -3.5) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-6 - 6)² + (5 - -3.5)²}
d =√{144 + 72.25}
d = √216.25
d = 14.71 units
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In 2010 an item costs $9.00. The price increases by 1.5% each year. How much will it be in 2020?
Answers
The term is actually forming an AP.
On 2010 = $9 = a
[tex] \frac{1.5}{100} \times 9 \\ = \frac{13.5}{100} \\ = 0.135[/tex]
d = $0.135
now on 2020, that's 10 years after 2010.
n = 10
[tex]an = a + (n - 1)d \\ = 9 + (10 - 1)0.135 \\ 9 + 9(0.135) \\ = 9 + 1.215 \\ = 10.215[/tex]
THE FINAL ANSWER - $10.125Please don't forget to mark braini if u are satisfied with answerthere might be another ways to solve this problem, but the simplest way is AP.Which descriptions and equations could be the function rule? Select all that apply. The table in attached image shows some of the input and output values for a function rule.
Answers
For the given table of values the equation that could be the function rule is option 4: y = 3x - 2.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The table of input and output values are given for the function.
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-2 - (-11)]/[0 - (-3)]
(-2 + 11)/(0 + 3)
9/3
3
So, the slope point is obtained as m = 3.
The equation becomes - y =3x + b
To find the value of b substitute the values of x and y in the equation -
-11 = 3(-3) + b
-11 = -9 + b
b = -11 + 9
b = -2
So, the value for b is -2.
Now, the equation becomes -
y = 3x - 2
The graph is plotted for the function.
Therefore, the equation is y = y = 3x - 2.
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Sylvan solved the division problem below. He made a mistake in his method. 1.6 divided by 0.4 with quotient 0.4. Subtract 1.6 from 1.6. Zero left over. A. What is the mistake that Sylvan made solving the problem?
Answers
Sylvan made a mistake computing the quotient in the problem.
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given here: 1.6 divided by 0.4
We know 1.6 can be expressed as 1.6=0.4×4
x ÷ y = z.
1.6÷0.4=4
Division method is nothing but the inverse of multiplication.
Divide 1.6 by number 0.4.
Solution:1.6÷0.4=1.6/0.4 with remainder zero
=4
Thus the quotient should have been 4
But according to Sylvan 1.6/0.4=0.4 which is not correct.
Hence, Sylvan computed the wrong quotient.
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Which tables represent functions? Select all that apply.
Group of answer choices
x y
-2 -2
-1 0
-2 3
2 5
x y
4 -2
1 -1
0 0
4 2
x y
-3 -9
-1 -3
0 0
5 15
x y
0 -2
2 0
3 1
7 5
Answers
Answer:
3 and 4
Step-by-step explanation:
numbers don't repeat in the X side
Move a number to each box to create an equation to solve 8/100+9/10 =
Answers
The solution of the given fraction can be gotten through filling the boxes with the following values respectively;
8/100 + 9/10 = 98/100
What is a fraction?A fraction is defined as the representation of a part of a whole value in the form of a numerator and denominator.
The given fraction;
8/100 + 9/10 = ?
Find the lowest common multiple of the denominator = 100.
= 8/100 + 9/10
= 8 + 90/100
= 98/100
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Which term is missing in this problem?
2x3 + 5x2 + 9
x + 3
Answers
After performing the division , the missing term in the problem is (2x³ + 5x² + 9)/(x + 3) = (2x² -x +3) .
The problem is (2x³ + 5x² + 9)/(x + 3) ;
that means , we have to divide , the expression "2x³ + 5x² + 9" by "x + 3" ;
first we multiply (x+3) by 2x² ;
the expression becomes : 2x³ + 5x² + 9
-2x³ - 6x²
-x² + 9
next we multiply by -x : -x² - 3x
3x + 9
next we multiply by 3 : -3x - 9
0 .
So , dividing the "2x³ + 5x² + 9" by "x + 3" , we get the remainder is 0 and the quotient is 2x² - x + 3 .
Therefore , the missing term is 2x² - x + 3 .
The given question is incomplete , the complete question is
Which is the missing term in this problem ?
(2x³ + 5x² + 9)/(x + 3) = ______ ;
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12.) Solve the right triangle. Round answers to the nearest tenth. To receive full credit you must show all work. M 8 40° K L 2 Solve the right triangle Bound answers to the nearest tonth KL = ML = mZK =
Answers
Answer: KL = 6.1, MK = 5.2 and the angle mZK = 40.
Step-by-step explanation: In this problem, to solve for the remaining sides and angles of the triangle, we can use trigonometry.
First, let's use the sine function to find the value of KL:
sin(40) = KL/ML
KL = (sin(40))(ML)
KL = (sin(40))(8)
Next, let's use the cosine function to find the value of MK:
cos(40) = MK/ML
MK = (cos(40))(ML)
MK = (cos(40))(8)
Finally, let's use the tangent function to find the value of mZK:
tan(40) = KL/MK
mZK = tan(40)
To round the answers to the nearest tenth, we can use the function Math.round(x * 10) / 10 in Javascript.
sin(40) = 0.766
cos(40) = 0.644
tan(40) = 1.193
KL = (0.766)(8) = 6.128 ≈ 6.1
MK = (0.644)(8) = 5.152 ≈ 5.2
mZK = 1.193
So the triangle KL = 6.1, MK = 5.2 and the angle mZK = 40.
Answer:
To solve the right triangle, we can use the trigonometric ratios sine, cosine, and tangent.
Given:
angle K = 40°
ML = 8
KL = 2
We can use the sine function to find the value of angle M:
sin(M) = KL / ML
sin(M) = 2 / 8
sin(M) = 0.25
So M = arcsin(0.25) = 14.04 (approximately)
Next, we can use the cosine function to find the value of MK:
cos(M) = ML / KL
cos(M) = 8 / 2
cos(M) = 4
So MK = 4
Lastly, we can use the tangent function to find the value of angle L:
tan(L) = KL / MK
tan(L) = 2 / 4
tan(L) = 0.5
So L = arctan(0.5) = 26.57 (approximately)
So the triangle is ML = 8, KL = 2, and angles M = 14.04° and L = 26.57° rounded to the nearest tenth.
x-y = -8 7x + 5y = 16
Which one is correct?
(8,16) or (-2,6)
Please explain how you got the answer.
Answers
Answer:
I think it is (8,16).
X 3 6 9 12 y 1 5 10 12 What is the r.o.c? Is this linear?
Answers
The rate of change is given a 5 / 6. The values we have here are not linear
How to solve for the rate of changeThe rate of change (r.o.c) is the change in y (or the dependent variable) for every unit change in x (or the independent variable). In this case, the r.o.c is
(10-5) / (12-6) = 5/6.
This is not linear because linear is a relationship between a variable and a constant, here the relationship between y and x is not linear because the change in y is not constant with respect to the change in x.
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Determine the intercepts of the line.
Do not round your answers.
3x+2y=5
Answers
Answer:
x intercept = 1.66666...
y intercept = 2.5
The x intercept is approximate. The 6's go on forever. The y intercept is exact without any rounding done to it.
======================================
Explanation:
Plug in y = 0. Then solve for x to get the x intercept.
3x+2y = 5
3x+2*0 = 5
3x = 5
x = 5/3
x = 1.66666...
The 6's go on forever.
------------------
Plug x = 0 into the equation and solve for y. This will get us the y intercept.
3x+2y = 5
3*0+2y = 5
0+2y = 5
2y = 5
y = 5/2
y = 2.5
This value is exact without any rounding
x = 5/3 or 1 2/3
y = 5/2 or 2 1/2
Step by step
To solve for x and y intercepts:
For x, sub 0 in for y and solve
For y, sub 0 in for x and solve
USE the figure to complete the statement if not similar choose not similar
Answers
Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
In triangle ΔABC, angle ∠B = 86° and ∠C = 55°, then angle ∠A is given as,
∠A + ∠B + ∠C = 180°
∠A + 86° + 55° = 180°
∠A = 39°
In triangle ΔDEF, angle ∠D = 55° and ∠F = 40°, then angle ∠E is given as,
∠E + ∠F + ∠D = 180°
∠A + 40° + 55° = 180°
∠A = 85°
Only one angle of the triangles ΔABC and ΔDEF is congruent. Then the triangles ΔABC and ΔDEF are not similar to each other.
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the fourth graders at pleasant grove elementary school voted for a new school mascot. wyatt the wolf got 90 votes. that is 9 times as many votes as bobby the bobcat got. how many votes did bobby the bobcat get?
Answers
335 students of fourth graders voted for the Falcon.
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. Similar to real numbers and whole numbers, a fractional number also holds some of the important properties. They are:
Commutative and associative properties hold true for fractional addition and multiplication
The identity element of fractional addition is 0, and fractional multiplication is 1The multiplicative inverse of a/b is b/a, where a and b should be non zero elementsFractional numbers obey the distributive property of multiplication over additionUsing proportions, it is found that 335 students voted for the Falcon. In total, 536 students voted for a mascot. The proportion that voted for the Falcon is 5/8 of the total number of students. To find the number of students that voted for the Falcon, we multiply the proportion of 5/8 by the total of 536, thus: 335 students voted for the Falcon.
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John makes $8 per hour walking dogs and $16 per hour as a math tutor. This weekend, he wants to work no more than 10 hours. He also wants to earn at least $96. Create a system of inequalities to model this
Answers
John must work 8 hours walking the dog and 2 hours as a Maths tutor in order to earn at least $96.
Let us assume that m represents the number of hours he walks the dogs
and n represents the number of hours he works as a maths tutor
John wants to work no more than 10 hours.
As we know the statement 'No more' is represented by the inequality '≤'
So, we get an inequality
m + n ≤ 10 ...........(1)
Also, he also wants to earn at least $96.
As we know the statement 'at least' is represented by the inequality '≥'
So, we get an inequality
8m + n ≥ 96 ...........(2)
So, we get a system of inequalities:
m + n ≤ 10
8m + n ≥ 96
Now, we solve this system of inequalities.
Consider m + n = 10 .........(3)
and 8m + n = 96 .........(4)
Substitute m = 10 - n for x in Equation 4
8(10 - n) + 16n = 96
80 - 8n + 16n = 96
8n = 96 - 80
n = 2
Substitute above value of n in equation m = 10 - n
m = 10 - 2
m = 8
Thus, John must work 8 hours walking the dog and 2 hours as a Maths tutor.
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The complete question is:
John makes $8 per hour walking dogs and $16 per hour as a math tutor. This weekend, he wants to work no more than 10 hours. He also wants to earn at least $96. Create a system of inequalities to model this and solve.
Does anyone know the answer?
Answers
Answer:
b or c
Step-by-step explanation:
126+6x=180
180-126=54
54/6=9
x= 9
PLS HURRY ITS TIMED Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range. y = x squared + 2 x minus 5 a. D: all real numbers R: (y less-than-or-equal-to negative 6) c. D: all real numbers R: (y less-than-or-equal-to negative 5) b. D: all real numbers R: all real numbers d. D: all real numbers R: (y greater-than-or-equal-to negative 6)
Answers
The graph of the quadratic function y = x² + 2x - 5 is given by the image at the end of the answer.
The domain and range are given as follows:
Domain: all real values.Range: y >= -6.How to obtain the domain and the range of the function?The domain of a function is the set that contains all the possible input values for the function, hence in the graph it is composed by the values of x of the function.
The range of a function is the set that contains all the possible output values for the function, hence in the graph it is composed by the values of y of the function.
More can be learned about domain and range of functions at https://brainly.com/question/30348593
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