Hello,
I hope you and your family are doing well!
Let's call Sydney's age x and Devaughn's age y. We know that y = 3x and x + y = 116.
Substituting the first equation into the second equation gives:
3x + x = 116
4x = 116
x = 29
So Sydney's age is 29.
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Happy Holidays!
21 =6/11 a +3
Pls hurry I need this like by tonight, btw 6/11 is a fractionnn
Answer: a=33
Step-by-step explanation:
Answer:
a=33
Step-by-step explanation:
1. Multiply both sides of the equation by 11
231=6a+33
2. Move 6a to the left side by subtracting
231-6a=33
3. Move 231 to the right side by subtracting
-6a=33-231
4. Find the difference
-6a=-198
5. Divide -6 on both sides to get "a" by itself
a=33
Graph the following features:
Y intercept =-2
Slope =-2/3
3
If f (x) = √2-x and g(x) = x-1, then find the domain of h (x) = f(x) = g(x).
O A.
(-∞0, 1) U (-1,2]
O B.
(-∞0, 1) U (1,2]
O C.
(-∞0, 2) U (1,2]
O D.
(-∞, -1) U (1,2]
O E. (-∞0,-2) U (1,2]
Reset
Next
Answer: B. ( - ∞ , 1 ) U ( 1, 2]
Step-by-step explanation:
The equation of H(x) is [tex]\frac{\sqrt{2-x} }{x-1}[/tex]
For the bottom denominator, x-1 cannot equal zero
x-1=0
x=1
For the numerator, 2-x square root has to be greater or equal to zero.
[tex]2-x\geq 0[/tex]
[tex]x\leq 2[/tex]
so the domain is
( - ∞ , 1 ) U ( 1, 2]
the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row. how many different arrangements of the display are possible?
Different arrangements of the display are possible is 2520.
Given:
the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row.
Permutation :
A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.
= [tex]7_P_5[/tex]
we know that,
[tex]n_P_r[/tex] = n! / ( n - r ) !
[tex]7_P_5[/tex] = 7! / ( 7 - 5 ) !
= 7! / ( 2 ) !
= 7! / 2!
= 7 * 6 * 5 * 4 * 3 * 2! / 2!
= 42 * 20 * 3
= 840 * 3
= 2520
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Magan went to the grocery store and purchased cans of soup and frozen dinners.
Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of
sodium. Magan purchased a total of 11 cans of soup and frozen dinners which
collectively contain 4750 mg of sodium. Determine the number of cans of soup
purchased and the number of frozen dinners purchased.
The number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, the can of soup contains 350 mg of sodium and the frozen dinner contain 650 mg of sodium.
Let the numbers of cans of soups and frozen dinners purchased be s and f, then,
s + f = 11
s = 11-f (1)
The total sodium in all 11 cans is 4750 mg which can be expressed as:
350s + 650f = 4750
Substitute s = (11-f) into the above equation:
350(11 - f) + 650f = 4750
3850 - 350f + 650f = 4750
300f = 4750 -3850
300f = 900
f = 3
Substitute f = 3 into equation (1):
s = 11-3
s = 8
Hence, the number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.
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Find the value of x.
It’s using the intersecting secant formula for exteriors but I keep getting decimals and it’s wrong.
Answer:
x = 7
Step-by-step explanation:
x(XY) = 6(WX)
x(x + 11) = 6(6 + 15)
x² + 11x = 126
x² + 11x - 126 = 0
126 = 7 × 18
(x + 18)(x - 7) = 0
x + 18 = 0 or x - 7 = 0
x = -18 or x = 7
We discard the negative answer.
x = 7
A postage box should weigh 1.0 punds. If there is a 5% error on the weight, what is the range of acceptable weight
Answer:
0.95-1.05 (please give brainliest)
Step-by-step explanation
1x.95=.95
1x1.05=1.05
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.
Refer to the attachment for graph.
What are vector equations ?
Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.
Given vector equation:
r(t) = < t², t, 2 >
When t= -2,
r(-2) = < (-2)², -2, 2 >
= < 4, -2, 2 >
This means. when t= -2, the curve touches the point ( 4, -2, 2 )
Similarly, when t= -1, the curve touches the point ( 1, -1, 2 )
Table is attached.
graph is attached.
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(8.08) Graph the first six terms of a sequence where a1 = 3 and d = −10. (2 points) Group of answer choices graphed sequence showing point 1, negative 10, point 2, negative 7, point 3, negative 4, point 4, negative 1, point 5, 2, and point 6, 5 graphed sequence showing point 1, negative 7, point 2, negative 4, point 3, negative 1, point 4, 2, point 5, 5, and point 6, 8 graphed sequence showing point 1, 3, point 2, negative 7, point 3, negative 17, point 4, negative 27, point 5, negative 37, and point 6, negative 47 graphed sequence showing point 1, negative 7, point 2, negative 17, point 3, negative 27, point 4, negative 37, point 5, negative 47, and point 6, negative 57
The first six terms of the given sequence are given as 3, -7, -17, -27, -37 and -47.
What is an arithmetic sequence?An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.
This difference is known as the common difference of the sequence.
The given problem can be solved as follows,
The first term of the sequence is a₁ = 3
And, the common difference is d = -10.
Now, the first six terms can be written as,
a₁ = 3
a₂ = 3 - 10
= -7
a₃ = -7 - 10
= -17
a₄ = -17 - 10
= -27
a₅ = -27 - 10
= -37
a₆ = -37 - 10
= -47
They can be graphed on the number line as follows,
Hence, the first six terms are given as 3, -7, -17, -27, -37 and -47.
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A bag contains 1 orange, 1 yellow, and 2 blue balls. The balls are replaced after each selection.
Draw a sample space to find the probability that the two selected balls are an orange ball and a blue ball.
The probablity that the two balls are orange and blue is 1/8
Describe Probability:
This is the chance or likelihood that an event will take place.
One orange ball, one yellow ball, and two blue balls are there in a bag.
The total number of sample space or outcome can be given as
Total outcome = 1 + 1 + 2=4
Probablity of occouring an orange ball can be given as, 1/4
Probablity of occouring a blue ball can be given as, 2/4
Probablity of an orange ball and a blue ball = 1/4 * 2/4
Probablity of an orange ball and a blue ball = 1/8
Consequently, there is a 1/8 chance that the two chosen balls are orange and blue
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Simplify each expression. Then drag and drop the equivalent matching expression.
3a+b+13a
20b+11a-5b
20b-5b+2b
You will not use all of the expressions.
From the expression, when simplified, (1) 16a+b (2) 17b+11a (3) 17b.
How to simplify algebraic expressions?An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.
The given algebraic terms are
3a+b+13a
Collect the like terms
3a+13a+b
Add the like terms
16a+b
Therefore, 3a+b+13a matches 16a+b
20b+11a-3b
Collect like terms
20b-3b+11a
=17b+11a
Therefore, 20b+11a-3b matches 17b+11a
20b-5b+2b
All the terms are alike, therefore do the arithmetic operation
15b+2b
=17b
Therefore, 20b-5b+2b matches 17b
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The ratio of of distance between two places A and B and B to C is 4:5. If the distance between A to C is 72 km, find the distance between A to B.
the whole distance containing all three points will be AC, and we know that AC = 72 km, now point B is between splitting the AC segment into AB and BC to a 4 : 5 ratio.
well, hell for that let's simply grab the total amount of 72 and split it up by dividing it by (4 + 5) and distribute accordingly.
[tex]A\stackrel{\text{\LARGE 4}}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\text{\LARGE 5}}{\rule[0.35em]{14em}{0.25pt}} C \\\\\\ \stackrel{AB}{4}~~ : ~~\stackrel{BC}{5} ~~ \implies ~~ \stackrel{AB}{4\cdot \frac{72}{4+5}}~~ : ~~\stackrel{BC}{5\cdot \frac{72}{4+5}} \\\\\\ \stackrel{AB}{4\cdot 8}~~ : ~~\stackrel{BC}{5\cdot 8} ~~ \implies ~~ \stackrel{AB}{\text{\LARGE 32}}~~ : ~~\stackrel{BC}{40}[/tex]
Pablo bought 13 pounds of flour for 8$ how many pounds of flour did he get per pound
The amount of flour he get in per dollar will be;
⇒ 1.625 dollars
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Pablo bought 13 pounds of flour for $8.
Now,
Since, Pablo bought 13 pounds of flour for $8
Hence, The amount of flour he get in per dollar = 13/8
= 1.625 pounds
Thus, The amount of flour he get in per dollar will be;
⇒ 1.625 dollars
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PLEASE HELP
A parking garage bases its
prices on the number of hours
that a vehicle parks in the
garage.
The first two hours cost $2 per
hour, between two hours and
six hours cost $2 per hour, and
all hours after that cost $1.
b
The first two hours cost $2 per
hour, between two and four
hours cost $1 per hour, and all
hours after that cost $0.50.
C
The first two hours cost $4.
between two hours and six
hours cost $2 per hour, and all
hours after that cost $1.
à
The first two hours cost $4.
between two hours and six
hours cost $1 per hour, and all
hours after that cost $0.50.
Answer:
Option C
The first two hours cost $4. Between two hours and six hours cost $2 per hour, and all hours after that cost $1.
Step-by-step explanation:
From the first part of the graph we can see that there is a flat rate of $4 for the first two hours. So the first two hours cost $4.
We can eliminate options A and B leaving C and D as only possible options.
Look at the second part of the graph
Between 2 hours and 6 hours(difference of 4 hours), the cost increases from $4 to $8 or an increase of $8
So rate per hour is $8/4 = $ 2 per hour between 2 hours and 6 hours
This information alone is enough to eliminate D but let's go to the rate beyond 6 hours just to make sure. This is the third part of the graph
Between 6 and 7 hours (1 hour) we can see the cost goes from $12 to $13 or a difference of $1. This means for every hour after 6 hours, the rate is $1 per hour.
So option C is the correct choice
The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37 and the probability plot support the assumption that the population is normally distributed. Construct a 95% two-sided confidence interval for ?.
A 95% two-sided confidence interval is 0.46 < a <0.31 .
The formula for confidence interval for population standard deviation is,
[tex]s\sqrt{\frac{n-1}{X^{2} _{1-a/2,n-1} } }[/tex] < a < [tex]s\sqrt{\frac{n-1}{X^{2} _{a/2,n-1} } }[/tex]
Given in question,
Significance level, a = 1 - 0.95
= 0.05
Sample size, n = 51
Sample standard deviation, s = 0.37
By using chi-square distribution table, we get
[tex]X^{2} _{1-a/2,n-1}[/tex] = [tex]X^{2} _{0.975,50}[/tex]
= 32.36
[tex]X^{2} _{a/2,n-1}[/tex] = [tex]X^{2} _{0.025,50}[/tex]
= 71.42
Confidence interval for population standard deviation is :
[tex]0.37\sqrt{\frac{50}{32.36} }[/tex] < a < [tex]0.37\sqrt{\frac{50}{71.42} }[/tex]
0.45992018426 < a < 0.30958278534
Hence, a 95% two-sided confidence interval is 0.46 < a <0.31 .
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Warm Up:
When designing a survey, what is one of the first things you need to know? What would you ask yourself?
Answer: Come up with questions that make sence. That are good solvablequestions. Make sure that you are able to take data off of it to see how people result in it.
Step-by-step explanation:
Suppose the coefficient of determination is 0.81, and the sample slope is negative. Then the coefficient of correlation is: a) 0.85 b) -0.85 c) 0.91 d) -0.90
The coefficient of correlation is -0.90
The percentage of the dependent variable's variance that is predicted from the independent variable is known as the coefficient of determination or R squared method. It shows how much variety there is in the given data collection.
The range of the coefficient of determination, which is the square of the correlation(r), is 0 to 1.
The square of the correlation between the x and y variables is used to calculate the coefficient of determination in linear regression.
The dependent variable cannot be predicted from the independent variable if R2 is equal to 0.
The dependent variable can be accurately predicted from the independent variable if R2 is equal to 1.
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If the volume of a cone is 30pi³ and the radius is 5 cm, what is the height?
Answer:
h≈1.15cm is the correct answer
Answer: h is about 1.15 cm
Step-by-step explanation:
when - 10 is subtracted from x the result is 6
Answer:
(-10) - (-16) = 6
Step-by-step explanation:
help meeeeeeeeeee pleaseee
For an average intake of 2200 calories per day, the number of acres of land is approximately 2.
How to solve function?A function having the formula f(x) = ax' + b is said to be linear.
It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).
You would be given the value of f(x) and asked to locate x when solving a linear function.
C(x) is a variable that tells the number of calories consumed daily by a person
x is the number of acres that person own.
C(x) = 270ln(x+1)+1900
In the given question number of acres ask a person have who consumed 2200 calories in a day.
Therefore,
C(x)=2200
2200=270ln(x+1)+1900
2200-1900=270ln(x+1)
300=270ln(x+1)
300/270 = ㏑(x+1)
10/9 = ㏑(x+1)
x+1 = e^(10/9)
x+1 = 3.037
x= 3.037-1
x=2.037
x=2(round off)
Therefore, 2 acres of land a person can consume 2200 calories in a day.
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A line has a slope of -3/5 through which two points could this line pass
Answer:
(5,-3), (10,-6)
Step-by-step explanation:
To raise funds for the local animal shelter, a group of BYU-Idaho students sold collars and scratching posts. The first week they sold seven collars and 10 scratching posts and donated $299.83. The second week they sold nine collars and 18 scratching posts and donated $482.85. "Because it is difficult to make two different items, they want to sell only one item during the last two weeks of the fundraiser. They decide to sell only the item for which they can donate the most money per item sold.
By using simultaneous linear equation, it can be concluded that-
They should sell only scratching post during the last two weeks of the fundraiser
Third option is correct
What is simultaneous linear equation?
At first, it is important to know about linear equation.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a system of simultaneous linear equation needs to be solved
Let the cost of one collar be $x and the cost of one scratching post be $y
The first week they sold seven collars and 10 scratching posts and donated $299.83.
7x + 10y = 299.83 ..... (1)
The second week they sold nine collars and 18 scratching posts and donated $482.85.
9x + 18y = 482.85 .... (2)
Multiplying (1) by 9 and (2) by 5
63x + 90y = 2698.47 ..... (3)
45x + 90y = 2414.25 ... (4)
Subraction (4) from (3)
18x = 284.22
x = [tex]\frac{284.22}{18}[/tex]
x = $15.79
Putting the value of x in (1)
7 [tex]\times[/tex] 15.79 + 10y = 299.83
110.53 + 10y = 299.83
10y = 299.83 - 110.53
10y = 189.3
y = [tex]\frac{189.3}{10}[/tex]
y = $18.93
Since the cost of one scratching post is more than cost of one collars, they should sold scratching post during the last two weeks of the fundrasiser
Third option is correct
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Complete Question
The complete Question has been attached
Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specific point.2(x-2)^2 + (y-1)^2 + (z-3)^2 = 10 at (3,3,5,)(a) x+y+z=11(b) x-3=y-3=z-5
For the given surface ;
(a) the equation of the tangent is x + y + z = 11 ,
(b) equation of normal is (x - 3) [tex]=[/tex] (y - 3) = (z - 5) .
In the question ,
it is given that ,
the equation of the surface is 2(x-2)² + (y-1)² + (z-3)² = 10 ,
we have to find the equation of the tangent at (3,3,5) .
the partial derivative fₓ = 4(x -2)
[tex]f_{y}[/tex] = 2(y-1) and [tex]f_{z}[/tex] = 2(z-3) .
the partial derivatives at (3,3,5) will be fₓ = 4(3 -2) = 4
[tex]f_{y}[/tex] = 2(3-1) = 4 and [tex]f_{z}[/tex] = 2(5-3) = 4 .
Part(a)
the equation of tangent at the point (3,3,5) is
fₓ(x - x₁) + [tex]f_{y}[/tex](y - y₁) + [tex]f_{z}[/tex](z - z₁) = 0 ,
Substituting the values form above ,
we get ,
4(x-3) + 4(y-3) + 4(z-5) = 0
4x - 12 + 4y - 12 + 4z - 20 = 0
after simplifying , we have 4x + 4y + 4z = 44 .
dividing both sides by 4 ,
we get ,
x [tex]+[/tex] y [tex]+[/tex] z [tex]=[/tex] 11 .
Part(b) ,
the equation of Normal is ;
(x-x₁)/fₓ = (y-y₁)/ [tex]f_{y}[/tex] = (z-z₁)/ [tex]f_{z}[/tex]
(x - 3)/4 = (y - 3)/4 = (z - 5)/4
(x - 3) [tex]=[/tex] (y - 3) [tex]=[/tex] (z - 5)
Therefore , the equation of tangent is x + y + z = 11 , and equation of normal is (x - 3) = (y - 3) = (z - 5) .
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Solve the inequality -9x/11 - 7 < -5. x > x < - x < x > -
The disparity -9x/11 - 7 < -5 is x > -22/9
Explain about the inequality?The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.
Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality.
-9x/11 < 2 (add 7 to both sides) (add 7 to both sides)
-9x < 22 (multiply both sides by 11) (multiply both sides by 11)
x > 22/-9 Because you are dividing by a negative integer, change the sign.
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Answer: x > [tex]\frac{-22}{9}[/tex]
Step-by-step explanation:
To solve this inequality, we will isolate the variable, x, with inverse operations.
Given:
[tex]\frac{-9x}{11}[/tex]- 7 < -5
Add 7 to both sides of the inequality:
[tex]\frac{-9x}{11}[/tex] < 2
Multiply both sides of the inequality by 11:
-9x < 22
Divide both sides of the inequality by -9:
* note, we must "flip" the sign since we are dividing by a negative integer
x > [tex]\frac{-22}{9}[/tex]
Pretzelmania, Incorporated, issues 7%, 10-year bonds with a face amount of $70,000 for $70,000 on January 1, 2024. Interest is paid annually on December 31.
Cr Cash 4,900 which is Interest paid annually on December 31.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
Pretzelmania, Inc., issues 7%, 10-year bonds with a face amount of $70,000 $70,000 on January 1, 2015. The market interest rate for bonds of similar risk and maturity is 7%. Interest is paid annually on December 31.
January 1, 2015, bonds issued at par value
Dr Cash 70,000
Cr Bonds payable 70,000
June 30, 2015, first coupon payment
Dr Interest expense of 4,900
Cr Cash 4,900
Thus, Cr Cash 4,900 which is Interest paid annually on December 31.
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Pls answer as fast as you can, no pressure.
Pavel is designing a restaurant and wants a unique dining area to add to the interest of the design. He thinks that an obtuse isosceles triangle would fulfill this requirement. He has two lengths of railing already in his possession—one that is 12 meters in length and one that is 22.8 meters in length. If he wants to keep his obtuse isosceles triangle design, which railing should he order a duplicate of to create his dining area. Explain.
To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:
12 meters.
When does a set of three measurements can represent a triangle?A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.
The measurements in this triangle are given as follows:
Smallest: 12 meters.Largest: 22.8 meters.If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.
Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.
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Answer:
Step-by-step explanation:
To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:
12 meters.
When does a set of three measurements can represent a triangle?
A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.
The measurements in this triangle are given as follows:
Smallest: 12 meters.
Largest: 22.8 meters.
If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.
Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.
HOME VALUE The average value of a house changes over time. The average
values of a house in January in Denver, Colorado, for different years are as
follows: 2014, $254,000; 2015, $293,000; 2016, $338,000; 2017, $372,000.
a. Make a table.
b. Determine the domain and range of the relation.
c. Determine whether the relation is a function.
a. The table for the given data is as follows :
Year 2014 2015 2016 2017
Value (in $) 254000 293000 338000 372000
b. Domain and Range for the given relation is:
Domain : {2014, 2015, 2016, 2017}
Range : {254000, 293000, 338000, 372000}
c. From the table we observe that for each year it is having a unique value so it is related to the function.
What is Domain?
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
What is Range?
The range of a function is the set of values that the function assumes.
What is Relation?
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the items x and y come from different sets, then the objects are said to be connected
a. The table for the given data is as follows :
Year 2014 2015 2016 2017
Value (in $) 254000 293000 338000 372000
b. Domain and Range for the given relation is:
Domain : {2014, 2015, 2016, 2017}
Range : {254000, 293000, 338000, 372000}
c. From the table we observe that for each year it is having a unique value so it is related to the function.
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What is the square root of 144?
Answer:12
Step-by-step explanation:
Which system of linear inequalities is graphed?
x ≤ -2
y≤ -x-3
x< -3
y< -x-2
x<-2
y≤ -x+2\
x< -2
y≤-x -2
The system of linear inequalities is graphed is x < -2; y ≤ -x+2. Hence option c is the correct.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The graph consists of two inequalities.
Since the one graph line is solid, thus the inequality sign either "less than or equal" or "greater than or equal". The other one is dotted, thus it will be less than or greater than
First find the equation of line.
One line passes through the points (-2,0) and (0,-2).
The equation of line that passes through the point (a,0) and (0,b) is
x/a + y/b = 1
The equation of the line is x/(-2) + y/(-2) =1
x + y = -2
y = -x - 2
The equation of the inequality will be either y ≤ -x - 2 or y ≥ -x - 2.
Putting x =0 and y = 0 in y ≤ -x - 2
0 ≤ - 0 -2
0≤ -2 (false)
In the graph (0,0) does not include in the shaded region. Therefore the inequality is y ≤ -x - 2.
The second line is parallel to y-axis.
The equation of line will be x = a
The line passes through the point (-2,0)
Putting x = -2 and y =0 in x = a
-2 = a
Therefore the equation of the dotted line will be x = -2
The equation of the inequality will be either x > -2 and x < -2:
Putting x =0 and y = 0 in x < -2
0 < -2
0 < -2 (false)
In the graph (0,0) does not include in the shaded region. Therefore the inequality is x < -2.
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a farm has 22 cows and chicken altogether. Each cow has four legs, and each chicken has two legs. The farmer counted 62 legs total. How many cows are on the farm? How many chickens?
The number of cows are 9 and the number of chickens are 13.
Given that, a farm has 22 cows and chicken altogether.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let the x be the number of cows and y be the number of chicken.
Now, x+y=22 -------(I)
The farmer counted 62 legs total.
So, 4x+2y=62 -------(II)
Multiply equation (I) by 2, we get
2x+2y=44 -------(III)
Subtract equation (III) from equation (II), we get
4x+2y-(2x+2y)=62-44
⇒ 2x=18
⇒ x=9
Substitute x=9 in equation (I), we get
9+y=22
⇒ y=13
Hence, the number of cows are 9 and the number of chickens are 13.
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