The counter example for the system of equation is given by x + y = 1 ,
-x - y = 1 has the result 0 = 2 but ( 0, 2 ) is not the solution of the equation. It proves statement is false.
As given in the question,
Form the given system of equations , using elimination method to get the solution of the equation which shows the result 0 = 2 is as follow:
a. x + y = 1
- x - y = -1
0 = 0
Not the required result.
b. x + y = 1
x - y = 1
2x = 2
Not a required result.
c. x + y = 1
- x - y = 1
0 = 2
Required result.
Analyze : substitute x = 0 and y = 2 in any one equation
0 + 2 = 1
or -0 -2 = 1
Both the equations proves that statement is false.
d. x + y = -1
-x -y = -1
0 = -2
Not a required result.
Therefore, the system of equation of option c. x + y = 1 , -x - y = 1 has the result 0 = 2 and proves it is the false statement.
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Which of the following relations are functions? Select all that apply.
A.
B.
C.
D.
Answer: first, second, and third images.
Step-by-step explanation:
to determine if something is a function, the domain must not have more than one answer in the range. My class calls it the y axis test, if you were to graph it, you cannot draw a line straight down that will go through two points. it's easy to understand with images like these, because all you need to know is that arrows cannot go from one number on the left to multiple on the right. Vice versa is a function, because it passes the y axis test.
Adrian bought 9 bags of chips for $29.25. What is the cost of a bag of chips, in dollars, if all the bags cost the same
Answer:
$3.25
Step-by-step explanation:
This is division
29.25 divided by 9
9 goes into 29.25 3 times
29.25-27=2.25
2.25 is 1/4 of 9
2.25*4=9 because 2*4=8 and .25*4=1 so 8+1=9
So the answer is 3 1/4 or $3.25
4 cups of peanut butter are needed to make 80 peanut butter cookies. Farwa wants to make 400 cookies. How many cups of peanut butter does she need?
Answer:
Step-by-step explanation:
400 ÷ 80
Number of cookies Divde by Number of peanut butter cookies
= 5 Total cups
Glenwood High School is constructing a new concrete basketball court that will need 60 cubic yards of concrete. When mixed, one bag of concrete will fill 0.5 cubic yards. The school ordered more than enough concrete to completely fill in the court. Let x represent how many bags of concrete the school ordered. Which inequality describes the problem?
Answer:
The school ordered more than enough concrete to completely fill in the court, so the number of bags of concrete ordered, represented by x, must be greater than the number of cubic yards of concrete needed to fill the court. This can be represented by the inequality x > 60 cubic yards / 0.5 cubic yards/bag. Solving for x, we get x > 60 * 2 = 120. Therefore, the inequality that describes the problem is x > 120.
What is true about the angles in the diagram shown below?
Triangle A B C is shown. Segment D E goes from side A B to side A C forming triangle A D E. Angle A E D and angle A C B have right angle labels. Angle A is labeled x degrees. Angle B is labeled three x degrees.
Enter the correct answers in the boxes.
The value of x is
.
The measure of ∠ADE is
°.
The measure of x is 22.5 and the angle ADE is 67.5 degrees
How to determine the value of x?The complete question is added at the end of this solution as an attachment
From the question, we have the following angle measures that can be used in our computation:
Angle A = x
Angle B = 3x
The sum of angles in a triangle is 180
So, we have
x + 3x + 90 = 180
Evaluate the like terms
4x = 90
Divide by 4
x = 22.5
How to determine the value of ADE?From the attached figure, we have
Angle ADE = Angle B
So, we have
Angle ADE = 3x
This gives
Angle ADE = 3 x 22.5
Evaluate
Angle ADE = 67.5
Hence. the angle is 67.5 degrees
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Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of 24 points and made 2 more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made, x,x, and the number of three point shots made, yy.
Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of 24 points and made 2 more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made, x, and the number of three point shots made, y.
x = the number of two point shots made
y = the number of three point shots made
Each two point shot scores 2 points, so x two point shots would score 2x points. Each three point shot scores 3 points, so y three point shots would score 3y points.
Therefore, the total number of points scored 2x + 3y equals 24 :
2x+3y=24
Since Landon made 2 more two point shots than three point shots, if we add 2 to the number of three point shots made, we will get the number of two point shots made, meaning x equals y + 2.
x = y + 2
Write System of Equations:
2x + 3y = 24
x = y + 2
Solve for y in each equation:
Which graph correctly shows the solution to the inequality 7x - 3/9 more than or equal to 8 - 2x
x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
(7x - 3)/9 more than or equal to 8 - 2x
(7x-3)/9 ≥ 8-2x
7x-3 ≥ 9(8-2x)
7x-3 ≥ 72-18x
Add 18x on both sides
7x+18x-3 ≥ 72
25x-3 ≥ 72
Add 3 on both sides
25x ≥ 75
Divide both sides by 25
x ≥ 3
Hence, x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.
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Solve equation:
3 + 7(6 +2x) = 157
We move all the characters to the left:
3+7(6+2x)-(157)=0We add all the numbers and all the variables.
7(2x+6)+3-157=0We add all the numbers and all the variables.
7(2x+6)-154=0Multiply
14x+42-154=0We add all the numbers and all the variables.
14x-112=0We move all terms containing x to the left side, all other terms to the right side
14x=112x=112/14x=8Answer:
x = 8
Step-by-step explanation:
Which equation is equivalent to the formula m=ca
The equivalent equation for the given equation m = ca is a = m/c. The equivalent equation has no effect on the original equation's actual function.
What is an equivalent equation?An equivalent equation is one that yields the same solution as the original equation.
The equivalent equation is obtained by removing a variable from the given equation. There will be the same number of equivalent equations as there are variables in an equation.
Given that,
m = ca
Here m, c, and a are the three variables in the given equation.
We can write the equation into two more forms as follows:
W.r.t variable 'c',
m = ca
Dividing both sides by 'a'
⇒ ca/a = m/a
c = m/a
W.r.t variable 'a',
m = ca
Dividing both sides by 'c'
⇒ ca/c = m/c
a = m/c
The missing image is attached with the answer.
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Mrs. Hudson's class of 18 students is going to the zoo. Each student will pay for admission and buy a lunch. Mr. Weaver's class of 24 students is going to the library. Each student will pay for admission and pay for bus fare. The costs are shown in the table for each field trip. The total cost for each group of students is the same.
The cost of admission to the library for each student will be $0.3125. And the admission cost of the zoo will be $156.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Mrs. Hudson's class of 18 understudies is going to the zoo. Every understudy will pay for confirmation and purchase lunch. Mr. Weaver's class of 24 understudies is going to the library. Every understudy will pay for affirmation and pay for transport passage.
Let 'x' be the cost of admission to the library for each student. Then the equation is given as,
$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24
Simplify the equation, then we have
$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24
$7.50 + $148.5 + $103.5 = 24x + $252
$259.5 - $252 = 24x
x = $0.3125
And the admission cost of the zoo will be given as,
⇒ $7.50 + $8.25 × 18
⇒ $156
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What is the is number rounded to the
nearest hundredth.
3.2369
Answer:
3.24
Step-by-step explanation:
The Hundredth is the second decimal place
Since 6 is greater than 5, round up
50 POINTSSSSSS ASAP!!!!
Quadrilateral RUST has a vertex at T (5, 2).
An image displaying a quadrilateral RUST.The vertex of R is R of 1 comma 5.
What are the coordinates of T' after the translation (x, y) → (x – 1, y + 2), followed by a dilation by a scale factor of 2, centered at the origin?
A.
(8, 8)
B.
(6, 2)
C.
(4, 4)
D.
(10, 4)
The coordinates of T' after the transformations are given as follows:
A. T'(8,8).
How to obtain the coordinates of the image of T?The coordinates of T are given as follows:
T(5,2).
Meaning that:
It has a x-coordinate of 5.It has a y-coordinate of 2.Then the translation is given as follows:
(x, y) → (x – 1, y + 2).
Meaning that the translated coordinates are of:
T'(5 - 1, 2 + 2) = T'(4, 4).
(as one was subtracted from the x-coordinate and 2 was added to the y-coordinate).
Then the dilation by a scale factor of 2 means that each of the coordinates is multiplied by two, hence:
T'(8,8).
Meaning that option A gives the correct coordinates of the image of the vertex T of the quadrilateral.
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Answer:
8,10
Step-by-step explanation:
i took the test
A taxi (yes, they still exist) charges a flat rate of $1.75, plus an additional $0.75 per mile. If you have at most $10 to spend on the cab ride, how far could you travel?
The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.
What is distance?
The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.
The formula for measuring distance between two lines, the total length of all a polygon's sides, the perimeter of a polygon on a coordinate plane, the area of a polygon, and many other things are all found in analytical geometry. For instance, we can use the distance formula to find the lengths of a triangle's sides and decide if it is scalene, isosceles, or equilateral.
It is given that, a taxi charges a flat rate of $1.75 plus an additional fee of $0.75 per mile.
We have to find the maximum distance it could travel at most with $10
Let the maximum distance be x miles.
Thus, the fare would be
$(1.75 + 0.75x) = 10
⇒ 0.75x = 8.25
⇒ x = 8.25/0.75
⇒ x = 11
The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.
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[] + (9+8) = (15x9) + (15x8)
The value of the equation A + ( 9 + 8 ) = ( 15 x 9 ) + ( 15 x 8 ) is 238
where A = 238
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as = P
Now , the value of P is given by
Let the unknown variable in the equation be A
A + ( 9 + 8 ) = ( 15 x 9 ) + ( 15 x 8 )
On simplifying the equation , we get
The value of A + 17 = 135 + 120
On adding the values in the equation , we get
The value of A + 17 = 255
On subtracting 17 on both sides of the equation , we get
The value of A = 238
Therefore , the value of A is 238
Hence , The value of the equation A + ( 9 + 8 ) = ( 15 x 9 ) + ( 15 x 8 ) is 238
where A = 238
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Find the slope of the line that passes through (1, 6) and (4, 24).
Answer:
y = 6x
Step-by-step explanation:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\frac{24-6}{4-1}[/tex]
[tex]\frac{18}{3}[/tex]
m = 6
y = mx + b
y = 6x + b
6 = 6(1) + b
6 = 6
b = 0
What is the combined mass of the Earth and Moon Express the answer in scientific notation
The combined mass of the Earth and Moon is 6.07342 × 10^24.
What is the combined mass of the Earth and Moon?Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.
Mass of Earth = 6 × 10^24
Mass of Moon = 7.342 × 10^22
The combined mass of the Earth and Moon will be:
= (6 × 10^24) + (7.342 × 10^22)
= 6.07342 × 10^24
The mass is 6.07342 × 10^24.
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what is the simplified form for (13-3/2r) - (1-r)????
Answer:
[tex]\frac{-r}{2} +12\\[/tex]
Step-by-step explanation:
Combine multiplied terms into a single fraction, find the common denominator, then combine fractions with the common denominator.
Which value of y is a solution of this inequality? 3y−4<11
Answer:
[tex]y<5[/tex]
Step-by-step explanation:
[tex]3y-4<11 \\ \\ 3y<15 \\ \\ y<5[/tex]
Determine which of the expressions could be used to represent the followi
Divide the difference between 96 and 72 by 12.
Select all that apply.
A. (96-72) 12
OB. 96 (72 ÷ 12)
C. (9612) 72
OD. 24 12
E. 96 ÷ 6
-
The difference between 96 and 72 by 12 can be expressed as
(96 - 72) / 12 and 24 / 12.
What is an expression?A mathematical expression is a sentence that contains at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all possible math operations.Monomial expressions are the most common type of algebraic expression. Expression of a binomial. Expression of a polynomial.We have to find the difference between between 96 and 72 by 12.
The difference between 96 and 72 can be expressed as,
96 -72
= 24
Next we have to divide the answer that is 24 by 12.
It becomes,
24/12
= 2
As a result, the required expressions for the following calculation is:
(96 - 72) / 12 and 24 / 12.
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. A fixed asset is purchased for Rs.1 lac with
excepted useful life of 5 years. Its depreciated
value at the end of 3rd year will be Rs.
If it is sold for Rs.45000, the firm will make
profit/loss of Rs.
Answer:
The profit or loss on selling a fixed asset will be
Step-by-step explanation:
We know that,
Depreciation = Original value - Scrap value / Estimated life of an asset
-> 100,000 - 0/ 5
= Rs 20,000 for every year
for 3 years,
Depreciation= 3 * 20,000 = Rs 60,000
The value of the asset after 3 years of depreciation = 100,000- 60,000
=Rs 40,000 ---(1)
If it is sold for Rs 45,000 ---(2)
Profit = (2) - (1)
= 45,000-40000
= Rs 5,000
Suppose the heights of a population of male giraffes are normally distributed with an unknown population mean and a population standard deviation of 3.4 feet. A random sample of male giraffes from the population produces a sample mean height of § = 15.2 feet.
What value of z should be used to calculate a confidence interval with a 90% confidence level?
Answer:
Step-by-step explanation:
Here we have:
90% confidence level:
α=1-0.90=0.10
[tex]Z_{crit}=z_{\alpha /2}=z_{0.10/2}=1.645[/tex]
Hence the required Z value at 90% confidence level is 1.645
Find the length of the third side. If necessary, round to the nearest tenth.
9. 5 I need the answer ASAP
Answer:
10.3 units------------------------
Let the missing side be x.
Use Pythagorean to find its value:
x² = 9² + 5²x² = 81 + 25x² = 106x = √106x = 10.295 ≈ 10.3 unitsIf the two bikes are racing a distance of 100 feet, which bike will win the race?
O Bike 2 will win because the slope of the line for Bike 2 is, which is greater than the slope of the line for Bike 1.
O Bike 2 will win because the slope of the line for Bike 2 is 5, which is greater than the slope of the line for Bike 1.
2
O Bike 1 will win because the slope of the line for Bike 1 is3, which is greater than the slope of the line for Bike 2.
O Bike 1 will win because the slope of the line for Bike 1 is , which is greater than the slope of the line for Bike 2.
If the two bikes are racing a distance of 100 feet, the bike that will win the race is: D. Bike 1 will win because the slope of the line for Bike 1 is 3/2, which is greater than the slope of the line for Bike 2.
How to calculate the slope of a straight line?Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would calculate the slope of the line representing the distance covered by each of the bikes based on the data points on their graph.
For Bike 1, the slope is given by;
Slope, m = (6 - 3)/(4 - 2)
Slope, m = 3/2
Slope, m = 1.5.
For Bike 2, the slope is given by;
Slope, m = (10 - 5)/(8 - 4)
Slope, m = 5/4
Slope, m = 1.25.
Therefore, the slope of Bike 1 is greater than the slope of Bike 2.
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help!!!! what’s number 2??
Answer:
Step-by-step explanation:
no
Answer: y= mb + xe
Step-by-step explanation:
4x²-14x+14x-49 factor by grouping
Answer:
x= 3.5 and x= -3.5
Step-by-step explanation:
4x^2 -49=0
x^2=49/4
x= 3.5 and -3.5
A grocery store has small bags of apples for $5 and large bags of apples for $7. If you buy 8
bags and spend $46, how many of each size bag did you buy?
Answer: 5 small bags and 3 large bags
Step-by-step explanation: 5+5+5+5+5=25 7+7+7=21 21+25=46
What is the value of x?
The midsegment has length 25 then the value of x exists 14.
What is meant by midsegment theorem?The length of the midsegment is half that of the base, according to the theorem.
A segment that joins the midpoints of two triangle's sides is referred to as a midsegment. According to the midsegment theorem, the third side of a triangle is parallel to the middle two sides of the triangle, and the midsegment is half its length.
Find the midpoints of two of any triangle's sides. A section joins these midpoints. This section will then be half the length of the third side and parallel to it.
The midsegment has length 25.
The base has length x.
x/2 = 25
simplifying the above equation, we get
x = 12.5
Therefore, the value of x exists 12.5.
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Given the function of f (x) = 2|x + 6| - 4 for what values of x is f (x) = 6
Answer:
2-23x
Step-by-step explanation:
PLS HELP ASAP! Which statement is true about the ratios comparing the width and length of each
The paintings' width to length ratios are equal because the ratio 9 to 6 is equal to the ratio 2 to 3.
The paintings' width to length ratios are different because the ratio 3 to 2 is not equal to 9 to 6.
The paintings' width to length ratios are equal because the ratio 6 to 9 is equal to the ratio 2 to 3.
The paintings' width to length ratios are different because the ratio 6 to 9 is not equal to 2 to 3.
The paintings' width-to-length ratios are different because the ratio 3 to 2 is not equal to 9 to 6. The correct option is B.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The width-to-length ratios of the paintings differ because 3 to 2 is not equal to 9 to 6.
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The table represents a quadratic function write an equation of the function in standard form
The function's standard form equation is equivalent to
y=(1/2)x²+(-7x)+24.
What is a quadratic function?A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.
The standard form of a quadratic equation in mathematics is represented by;
ax² + bx + c = 0
y=ax² + bx + c
The information in the table above would then be used to create a set of equations:
The points are (4, 4), (6, 0), (8, 0), (10, 4)
4=a(4)²+b(4)+c
16a+4b+c=4 ------(1)
0=a(6)²+b(6)+c
36a+64b+c=0 ------(2)
0=a(8)²+b(8)+c
64a+8b+c=0 -------(3)
By solving 2 and 3 equations, we get
Eq2-Eq3,
We get b= -14a
By substituting b value in eq2 we get,
36a+6b+c=0
36a+6(-14a)+c=0
35a-84a+c=0
c=48a
By substituting a, b values in eq1 we get,
16a+4(-14a)+48a=4
16a-56a+48a=4
-40a+48a=4
8a=4
a=1/2
Then, b=-14a
b= -7
c=48a
c=24
Now, by substituting these a, b, c values in,
y=ax² + bx + c
y=(1/2)x²+(-7x)+24
By checking the above equation is correct or not,
We consider the fourth value x=10
When x=10,
y=(100/2)-70+24
y=50-70+24
y=4
From the given table if x=10 then y=4,
So it satisfies with the equation we get.
Therefore, the function's standard form equation is equivalent to
y=(1/2)x²+(-7x)+24.
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