How many linear equations in two variables will have solutions x1 and Y 3?

The area of the shaded region is equal to 58 square units.

What is an area?

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of the shaded region will be calculated as,

Area of entire object= 10 units x 7 units= 70 units.

Area of the gap= 2 units x 6 units= 12 units.

The area of the shaded figure= is 70 units - 12 units= 58 units.

Therefore, the area of the shaded region is equal to 58 square units.

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Answer:

K = - 2J + 24

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept, where line crosses y- axis )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 24) and (x₂, y₂ ) = (6, 12) ← 2 points on the line

m = [tex]\frac{12-24}{6-0}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2

the line crosses the y- axis at (0, 24 ) ⇒ c = 24

y = - 2x + 24

convert y to K and x to J , in this case , then

K = - 2J + 24 ← equation of trend line

Dina is 10 years younger than Mimi, thus she is 8 years older after 3 years. Mimi will be twice as old as Dina in 5 years.

The device tactic is a method of addressing dilemmas that entails first figuring out the price of a specific unit, then multiplication that value to figure out the needed value. Simply put, the unit method is used to derive a single unit value from a multiple that is supplied. For example, 40 pens would cost 400 rupees, which is equal to the price of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, numerical modeling, or mathematics of matrices or operators.

given

Dina should be x years old, and Mimi should be x + 10 years old.

After five years,

Mimi's age is x+10 + five years, = x+15 years for Dina.

x+ 15 = 2 ( x+ 5 )

Dina will be old in 3 years when

x + 3 = 5 + 3 = 8 years since

x + 15 = 2x + 10 x = 5.

Dina is 10 years younger than Mimi, thus she is 8 years older after 3 years. Mimi will be twice as old as Dina in 5 years.

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The equation that represents the graph is y equals negative three halves times x minus 3, and option A is correct.

The ratio of the change in y coordinate to the change in x coordinate is known as a line's slope.

y and x, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.

Consequently, the connection between a change in y-coordinate and a change in x-coordinate

Given a graph,

from the graph, we find that when y is 0, x = -2

and when x is o, y = -3

so the line passes from (-2, 0) and (0, -3)

the slope of the line is (y₂-y₁)/(x₂-x₁)

m = (-3 - 0)/(0 - 2)

m = -3/2

and the y-intercept is -3

equation of line is y = mx + c

y = -3x/2 - 3

which is y equals negative three halves times x minus 3.

Hence option A is correct for the equation of the line,

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Answer:D

Step-by-step explanation:D

Answer:

88 cm

Step-by-step explanation:

the formula for circumference is π · d  

28 · 22/7 = 88

88 cm is the circumference of a circle with a diameter of 28 cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The circumference of a circle with a diameter of 28 cm.

Radius = 28/2

Radius is 14 cm.

Circumference=2πr

=2×3.14×14

=87.92=88 cm

Hence, 88 cm is the circumference of a circle with a diameter of 28 cm.

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The sum of the first 140 natural numbers of the given arithmetic sequence is; 9870

The formula to find the nth term of an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

The formula to find the sum of the n terms of an arithmetic sequence is;

Sₙ = ⁿ/₂(2a + (n - 1)d)

In this question, we see that;

a = 1

d = 1

n = 140

Thus;

S₁₄₀ = (140/2)(2(1) + (140 - 1)1))

S₁₄₀ = = 70(2 + 139)

S₁₄₀ = 9870

That is the sum of the first 140 terms in conclusion

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K Representations of transformations to represent a constant value the parent.

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Answer:

4.5 cups of flour now.

Step-by-step explanation:

Trevor has 7.375 - 2.875 = 4.5 cups of flour now.

Answer:

Trevor has 4 ½ cups of flour now.

Step-by-step explanation:

To find the amount of flour Trevor has after using 2 ⅞ cups, we need to subtract 2 ⅞ cups from 7 ⅜ cups.

7 ⅜ cups - 2 ⅞ cups = 4 ½ cups

So, Trevor has 4 ½ cups of flour now.

a) x > 11

b) j < 17

c) b => 9

d) h <= 104

e) k > -8/3

f) p < -24/5

g) q => -17/2

h) f <= 29.52

Answer:

Step-by-step explanation:

one of the answer is zero

Answer:

a) -3

b) 9

c)-15

d) 3

e)-21

Step-by-step explanation:

plug in the number given within parentheses into f(x) = 6x-3.

the answer is 33.125

Add or subtract both the linear equations such that the same terms will get eliminated.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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Answer: The answer to this question is 16.75.

Step-by-step explanation:

 16.40

+ 0.35            

 16.75

As the x-coordinate is negative and y-coordinate is zero ,Point (−4,0) lies on negative x-axis

Hey dear ,

I have just created graph for your

U can see that (4,0),(6,0),(8,0) lie on same line I. e X axis

Hence , they are collinear

they lie on a straight line which is the X axis as the y coordinate is zero

Here the x-coordinate of our point is −4 and the y-coordinate of our point is 0

As the x-coordinate is negative and y-coordinate is zero ,Point (−4,0) lies on negative x-axis

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The slope - intercept form of the function is given as y = 6.5x - 5

Slope-intercept form is a way of expressing the equation of a straight line in the form of:

y = mx + b

Where:

The slope-intercept form is so named because it shows the slope (m) and y-intercept (b) of the line explicitly. It is considered one of the most useful forms for working with and graphing lines, as it allows you to easily see the steepness of the line and where it crosses the y-axis.

The slope of a line is a number that describes how steep the line is. It is calculated as the ratio of the change in y to the change in x. A positive slope means that the line is rising as it moves from left to right and a negative slope means that the line is falling as it moves from left to right. A slope of zero means that the line is horizontal, and a slope that is undefined means that the line is vertical.

In this problem, we take the points and find the slope.

f(2) = 8

y₁ = 8, x₁ = 2

y₂ = -5, x₂ = 0

slope (m) = y₂ - y₁ / x₂ - x₁

m = -5 - 8 / 0 - 2

m = 6.5

Using the slope, we can calculate the y - intercept.

y = mx + c

-5 = 6.5(0) + c

c = -5

The slope-intercept form is y = 6.5x - 5

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Negative slope means that as we move from left to right on the graph, the line falls. Zero slope means that the line is horizontal: it neither rises nor falls as we move from left to right. Vertical lines are said to have "undefined slope," as their slope appears to be some infinitely large, undefined value.

Now, According to the question:

A line that slants up from left to right has a positive slope. A line that slants down from left to right has a negative slope. Horizontal and vertical lines also have a slope. A horizontal line has a change in x, but it does not have a change in y.

Negative slope means that as we move from left to right on the graph, the line falls. Zero slope means that the line is horizontal: it neither rises nor falls as we move from left to right. Vertical lines are said to have "undefined slope," as their slope appears to be some infinitely large, undefined value.

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The product of AXB is the matrix C, where Cij = Σk=1nAikBkj, where n is the number of columns in A.

The product of two matrices A and B is a new matrix C, which is obtained by multiplying each of the elements of A with the corresponding elements of B. The size of the resultant matrix C will be the same as that of A and B. For example, if A is m×n and B is n×p, then the product AXB will be an m×p matrix. The value of each element of C is determined by multiplying the elements of corresponding rows of A with those of corresponding columns of B, and then summing up the products. Mathematically, the value of Cij (the element in the ith row and jth column of C) is given by the equation

Cij = Σk=1nAikBkj,

where n is the number of columns in A.

The product of AXB is the matrix C, where Cij = Σk=1nAikBkj, where n is the number of columns in A.

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The ordered pair for option C) (1,3) is not a solution of the equation 2x+y =7.

A solution of an equation is a set of values for the variables that make the equation true.

In the case of a linear equation in two variables, such as ax + by = c, where a, b, and c are constants, the solution can be found by using techniques such as substitution, elimination, and graphing.

To find the solution of equation 2x + y = 7, we need to find the values of x and y that make the equation true.

a. (1,5): when we substitute the x = 1, y = 5 in equation 2x + y = 7, 2(1) + (5) = 7, 2 + 5 = 7, which is true so this pair is a solution.

b. (3,1): when we substitute the x = 3, y = 1 in equation 2x + y = 7, 2(3) + (1) = 7, 6 + 1 = 7, which is true so this pair is a solution.

c. (1,3): when we substitute the x = 1, y = 3 in equation 2x + y = 7, 2(1) + (3) = 5, 2 + 3 = 7, which is not true so this pair is not a solution.

d. (0,7): when we substitute the x = 0, y = 7 in equation 2x + y = 7, 2(0) + (7) = 7, 0 + 7 = 7, which is true so this pair is a solution.

Therefore, The ordered pair for option C) (1,3) is not a solution of the equation 2x+y =7.

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The solution is Option B.

The fraction of bookshelf Kiki painted is closer to 1/2

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the total fraction of bookshelf painted be A

Now , the value of A is

The fraction of bookshelf painted on Monday = 1/5 of total

The fraction of bookshelf painted on Tuesday = 5/6 of total

Now , the total bookshelf painted A = ( 1/5 ) + ( 5/6 )

The total bookshelf painted A = ( 6 + 5 ) / 30

On simplifying the equation , we get

The total bookshelf painted A = 11/30

The total bookshelf painted A = 0.36667

So , the value of A is closer to 1/2

Hence , the fraction is 11/30

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Your roommate can take 4 different collections of pets as he can't take both the dog and the cat.

The problem states that your roommate has six pets (fish, cat, turtle, dog, rock, and pony) and he wants to take three of them with him but he can't take both the dog and the cat because they will fight.

We can solve this problem using the combination formula which is (nCr) = n! / (r! * (n-r)!) where n is the total number of items and r is the number of items being chosen.

In this case, there are 6 pets and he wants to take 3 of them, but not the dog and the cat. So, we have 6-2=4 pets remaining.

So the number of different collections of pets he can take is (4C3) = 4! / (3! * (4-3)!) = 4! / (3! * 1!) = 4.

So, your roommate can take 4 different collections of pets as he can't take both the dog and the cat.

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The total cost of student ticket in the class of Ms. Green is $210 and the cost of student ticket in the class of Ms. White is $165.

In the given question, we have to find how much the student tickets for both classes cost in total.

Ms. Green and Mr. White took their science classes to the museum.

Let the cost of student ticket is x.

Let the cost of adult ticket is y.

Ms. Green spent $262 to buy 28 student tickets and 4 adult tickets for her class.

So the required equation is:

28x + 4y = 262...(1)

Mr. White spent $191 for 22 student tickets and 2 adult tickets for his class.

So the required equation is:

22x + 2y = 191...(2)

Multiply equation 2 by 2 then subtract by 1

44x + 4y - (28x + 4y) = 382 - 262

16x = 120

Divide by 16 on both side, we get

x = 7.5

Now putting the value of x in equation 1, we get

28(7.5) + 4y = 262

210 + 4y = 262

Subtract 210 on both side, we get

4y = 52

Divide by 4 on both side, we get

y = 13

Hence, the cost of student ticket is $7.5 and the cost of adult ticket is $13.

Now we have to find the total cost of student tickets in both classes.

The cost of student ticket in the class of Ms. Green = 28x

The cost of student ticket in the class of Ms. Green = 28×7.5

The cost of student ticket in the class of Ms. Green = $210

The cost of student ticket in the class of Ms. White = 22x

The cost of student ticket in the class of Ms. White = 22×7.5

The cost of student ticket in the class of Ms. White = $165

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The measure (in degrees) of the smallest interior angle of a triangle in which the exterior angle measures have the ratio 4:5:6 is 36°.

The exterior angles of a triangle measure the angle between one side of a triangle and the extension of an adjacent side. The sum of the exterior angles of a triangle is always equal to 360 degrees.

In a triangle in which the exterior angle measures have the ratio 4:5:6, we can express the measures of the exterior angles as 4x, 5x, and 6x.

360 = 4x + 5x + 6x

360 = 15x

Solve for x by dividing both sides by 15:

x = 360/15 = 24

Knowing that the measures of the exterior angles are 4x, 5x, and 6x, we can find the measure of the smallest interior angle by subtracting the biggest exterior angle from 180 degrees:

biggest exterior angle = 6x = 6(24) = 144°

smallest interior angle = 180° - 144° = 36°

Therefore, the measure of the smallest interior angle of a triangle in which the exterior angle measures have the ratio 4:5:6 is 36°

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The parametric equation of line is:

(x – x₁) / cosθ = r

and (y – y₁) / sinθ = r, where r is the parameter and θ is an angle made by straight line with x-axis.

We know that the parametric equation of a straight line passing through point (x₁, y₁) and which makes an angle θ with the positive X-axis is given by,

(x – x₁) / cosθ = (y – y₁) / sinθ = r,

where r is a parameter, which represents the distance between points (x, y) and  (x₁, y₁)

The parametric equations of the line are of the form:

x = x₀ + at,

y = y₀ + bt,

and z = z₀ + ct.

where the components a, b and c of are the direction numbers of the line.

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The equations are solved below.

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here:

[tex]y=10^{3x-5} \\y=e^{-5x+3} \\y=e^{-4x+1}[/tex]

Thus taking log both sides of the equations we get

[tex]1) y=10^{3x-5}=logy=(3x-5).1\\\\(logy+5 )/3=x \\ \\2)y=e^{-5x+3}=lny=-5x+3.1\\ x=(lny-3.1)/-5\\\\3) y=e^{-4x+1} \\x=(lny-1)/-4[/tex]

Hence, The equations are solved for the above equations in terms of y

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Answer: 20

Step-by-step explanation: 2 half triangles at the top can be made into 1 square of 4 units which added onto the other part to create 1, 4 by 5 shape which is 20

The correct answer is D. 3y + 5 − 7y = 4(-y + 1) + 5.

What is the solution of the equation?

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.

The equation that has no solution is D. 3y + 5 − 7y = 4(-y + 1) + 5.

This is because the left-hand side is equal to -4y + 5, while the right-hand side is equal to y + 10. These two expressions are not equivalent, so there is no value of y that makes the equation true.

For equations A, B and C, we can simplify the left and right sides of the equation and see that they are equivalent and thus have solutions.

Hence, The correct answer is D. 3y + 5 − 7y = 4(-y + 1) + 5.

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Answer:

-10m

Step-by-step explanation:

-2m-8m = -10m

Answer:

-10m

Step-by-step explanation:

a negative + a negative is still negative.

Hope this helps!

Answer:

0.043

Step-by-step explanation:

Answer:

dont

Step-by-step explanation: