Mrs.may mixed 4 gal of red paint with every 6 gal of blue paint in order to make purple paint. which ratio of gallons of red paint to gallons of blue pint will make the same shade of purple paint?

Angle, when two straight lines or rays intersect at a single endpoint,  then an angle is created.

The exterior angle of a triangle equals the sum of opposite interior angles. The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.

∠XYZ  = ∠YWX + ∠WXY

10x - 5   = 3x + 17 + 3x + 2

10x - 5 = 6x + 19

10x - 6x  = 24

4x  = 24

x = 6

∠WXY =  3x + 2

= 3*6 + 2

= 20°

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The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.

In mathematics, a circle is a geometric figure made up of all the points in a sphere that are equally spaced from the circle's centre. The radius of the circle is the distance measured from any location on the circle to its centre. The width of a circle is the distance across the circle that passes through its centre, and the circumference of a circle is the distance around the circle. The equations of circles in the coordinate plane can be used to characterise them. The equation for a circle with centre (h,k) and radius r has the following conventional form:

(x - h)² + (y - k) (y - k)² = r² where (x,y) are any location on the circle's coordinates.

given

We can begin by completing the cube to rewrite the equation in standard form:

x2 - 2x + y2 = 8

(x - 1)2 + y2 = 9

We can see from this standard shape that the circle's centre is (1, 0), which is located on the x-axis. This circular has a radius of √9 units, or 3 units. Thus, the following assertions are true:

The circular has a radius of three units.

The x-axis is where the circle's middle is located.

The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.

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As per the given digit value, 10 times the value of the 7 in 637.739 is 7.

To understand this problem, we need to understand the concept of place value. In our base-10 number system, each digit in a number has a specific value based on its position, or place, in the number. The rightmost digit represents the ones place, the next digit to the left represents the tens place, the next represents the hundreds place, and so on.

In the number 637.739, the digit in the tenths place is 7. This means that the 7 represents 7 tenths, or 0.7. We can see this by writing the number in expanded form:

6 hundreds + 3 tens + 7 tenths + 7 hundredths + 3 thousandths + 9 ten-thousandths

So, if we want to find 10 times the value of the digit in the tenths place (which is 7), we need to multiply 0.7 by 10:

0.7 x 10 = 7

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Answer:

y=2-2x

so y=2x+2--£8;£++£

Answer: y=−2x + 2

Step-by-step explanation:

Subtract 2x from both sides of the equation.

y= 2 − 2x

Reorder 2 and −2x.

y= −2x + 2

Answer:   35+63

The only way to label the expression without changing our numbers is 35+63. We still get the sum of 98 and the same numbers are being used, they are just in a different order.

I hope this helped and Good Luck <3!!!

$$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$

To compute the least squared error solution to \( A x=b \), we will use the formula \(x = (A^T A)^{-1} A^T b\).

In this case, \(A = \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\), so \(A^T = \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix}\). Therefore, we have that

$$(A^T A)^{-1} A^T b = \left(\begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\right)^{-1} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b$$

From here, we can compute the inverse of the matrix \(A^T A\) to get

$$(A^T A)^{-1} = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}$$

Substituting this into the equation above and multiplying through, we get

$$x = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}$$

Therefore, the least squared error solution to \( A x=b \) is $$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$

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Answer: Your welcome!

Step-by-step explanation:

Part A: 2x^2 + 3x^2 - 4 + 3xy + 6 + 6 = 7x^2 - 4xy + 6

Part B: 0 = 7x^2 - 4xy + 6 - (2x^2 + 3x^2 - 4 + 3xy + 6 + 6)

= 0 = 5x^2 - 4xy

A) The expression that represents the amount of canned food collected by the three friends is [tex]5x^2 + 3xy + 2[/tex].

B) The expression that represents the number of cans the friends still need to collect to meet their goal is [tex]2x^2 - 7xy + 4[/tex].

Given: Number of cans collected

Jessa: 2x²

Tyree: 3x² - 4

Ben: 3xy + 6

Goal : [tex](7x^2 - 4xy + 6)[/tex]

A) The total amount collected:

Total = Jessa + Tyree + Ben

         = [tex]2x^2 + (3x^2 - 4) + (3xy + 6)[/tex]

         = [tex]2x^2 + 3x^2 - 4 + 3xy + 6[/tex]

         = [tex](2x^2 + 3x^2 + 3xy) + (-4 + 6)[/tex]

         = [tex]5x^2 + 3xy + 2[/tex]

Therefore, the expression is [tex]5x^2 + 3xy + 2[/tex].

B) The number of cans the friends still need to collect to meet their goal is

Cans still needed = Goal - Total

                              [tex]= (7x^2 - 4xy + 6) - (5x^2 + 3xy + 2)[/tex]

                              [tex]= 7x^2 - 4xy + 6 - 5x^2 - 3xy - 2[/tex]

                              [tex]= (7x^2 - 5x^2) + (-4xy - 3xy) + (6 - 2)[/tex]

                              [tex]= 2x^2 - 7xy + 4[/tex]

Therefore, the expression is [tex]2x^2 - 7xy + 4[/tex].

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The values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.

The system has no solutions when the coefficients of the variables are the same but the constants are different. In this case, the coefficients of x, y, and z are the same in the first and second equations, but the constants are different (5 and 3). Therefore, there is no solution for a = -8.

The system has infinitely many solutions when the coefficients of the variables and the constants are the same in all equations. In this case, the coefficients of x, y, and z are the same in the first and second equations, and the constants are the same (5 and 5). Therefore, there are infinitely many solutions for a = 8.

The system has exactly one solution when the coefficients of the variables are different in all equations. In this case, the coefficients of x, y, and z are different in the first and second equations, and the constants are different (5 and 3). Therefore, there is exactly one solution for a ≠ ±8.

In conclusion, the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.

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Answer:

5 (3x+2)

Step-by-step explanation:

Hope this helps! :)

m - (8 - 3m)

m - 8 + 3m

m + 3m - 8

4m - 8

Answer:

Step-by-step explanation:

m-(8-3m)

m-8 + 3m

=m+3m-8

=4m-8

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

put the value of x = 4

[tex] \: [/tex]

[tex] \sf \: f( 4 )*g( 4 ) = 3(4)²*( 4 - 8 ) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3×16*(-4) \\ \sf \: \: \: \: \: \: \: \: \: \: \: = 48*( -4 ) \\ \: \: \: \: \underline{ \sf \red{ \: = -192 \: }}[/tex]

[tex] \: [/tex]

hope it helps! :)

Answer:

$948.34

Step-by-step explanation:

35% = .35

.35 x $2299

= $804.65

That is the total before the sales tax and after the sale.

6.25% = .0625

.0625 x $2299

= $143.69, and because that is 6.25% of the total, it must be added onto that as tax.

That means the total is $804.65 + $143.69

= $948.34

Answer:

34

Step-by-step explanation:

3dds

The property illustrated in "√2+√8 is a real number" is the closure property of addition,

The property illustrated in the given statement is the closure property of addition, which states that the sum of two real numbers is also a real number.

The closure property of addition states that the sum of any two real numbers is also a real number. In the given statement, √2 and √8 are both real numbers, and therefore their sum √2+√8 is also a real number.

This property applies to all real numbers, and it is an important property of the number system. which states that the sum of two real numbers is also a real number.

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Answer:

(-1.5, -112.5)

Step-by-step explanation:

f(n) = 2(n + 9)(n - 6) = 0

n = -9, n = 6

½(6 - (-9)) = ½(15) = 7.5

-9 + 7.5 = -1.5

f(-1.5) = 2(-1.5 + 9)(-1.5 - 6)

= 2(7.5)(-7.5)

= -(15 × 7.5)

= -(75 + 37.5)

= - 112.5

The value of x is 7

The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°

Therefore ;

50+28+15x-3 = 180

78-3 +15x = 180

75 +15x = 180

collect like terms

15x = 180-75

15x = 105

divide both sides by 15

x = 105/15

x = 7

therefore the value of the missing variable (x) is 7

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After factoring out, 4(5x+3y) simplifies to 20x + 12y.

The act of replacing a complex mathematical expression with a simpler equivalent is known as simplification (usually shorter).

An equivalent fraction is one in which the numerator and denominator are both divisible by the same non-zero number. If a fraction's numerator and denominator are both divisible by a number greater than 1, the fraction can be reduced to an equivalent fraction by reducing both its numerator and its denominator.

To simplify 4(5x+3y), we can use the distributive property of multiplication over addition:

4(5x + 3y) = 4(5x) + 4(3y)

Simplifying the multiplication:

4(5x + 3y) = 20x + 12y

Therefore, 4(5x+3y) simplifies to 20x + 12y.

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By answering the above question, we may state that As a result, the cylinder cylinder's volume is around 804.23 cubic centimetres.

The cylinder, which is frequently a three-dimensional solid, is one of the most fundamental curved geometric shapes. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinder" is also used to refer to an infinitely curved surface in a number of modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure with two bases that are both identical circles connected at its height, which is defined by the separation of the bases from the centre. Cans of iced drinks and the wicks from toilet paper are examples of cylinders.

The following is the formula for a cylinder's volume:

[tex]V = \pi r^2h[/tex]

where the volume is V, the radius is r, and the height is h.

Inputting the values provided yields:

[tex]V = \pi * 4^2 * 16 = 804.24[/tex]

To the closest hundredth, we round to:

V ≈ 804.24 ≈ 804.23 (rounded to two decimal places) (rounded to two decimal places)

As a result, the cylinder's volume is around 804.23 cubic centimetres.

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Answer: 26

Step-by-step explanation:

65x40%

calculate 65x0.4

    Please give me brainliest

Answer:

x = 3.92699081 + 7.85398163n where n is an integer

The distance between the landing pads is approximately 12.82 miles.

A straight line is the shortest distance between two points in a two-dimensional space. It is a one-dimensional geometric object that extends infinitely in both directions.

Let's label the distance between the helicopter and Pad A as "x" and the distance between the helicopter and Pad B as "y". Also, let's label the distance between Pad A and Pad B as "d".

We can start by using the tangent function to find the height of the helicopter above Pad A:

tan(46) = h / x

h = x tan(46)

Similarly, we can find the height of the helicopter above Pad B:

tan(16) = h / (x + d)

h = (x + d) tan(16)

Since the helicopter is flying at a constant height, we can equate the two expressions for h and solve for d:

x tan(46) = (x + d) tan(16)

xtan(46) = xtan(16) + dtan(16)

d = x(tan(46) - tan(16)) / tan(16)

Substituting x = 5 miles and the values for the tangent functions, we get:

d = 5 (0.9851 - 0.2760) / 0.2760

d = 5 (0.7091) / 0.2760

d = 12.82 miles

Therefore, the distance between the landing pads is approximately 12.82 miles.

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Answer: (0, 2)

Step-by-step explanation:

The solution of a system of equations is where the lines intersect at.

We will use substitution to solve the system.

Equations:

y = 1/2x + 2

y = -1/5x + 2

Set both equations to equal each other:

1/2x + 2 = -1/5x + 2

Simplify:

7/10x = 0

x = 0

Plug 0 back in:

y = 1/2(0) + 2

y = 0 + 2

y = 2

The solution is (0, 2)

(This can also be seen by looking at the graph)

Hope this helps!

Therefore, the distance from the center of the circle to the crossing point of the two strings is 40sqrt(2) cm, or approximately 56.57 cm to two decimal places.

The Pythagorean theorem can be used to calculate the distance between the circle's centre and where the two strings cross. Let A and B represent the spots where the threads converge, with O serving as the circle's centre. Next, we have:

OA2 plus OB2 equals AB2.

The circle's radius being equal to half the separation between the two strings, we get:

The equation OA = OB = sqrt((560/2)2 + (640/2)2) (156800)

And because the circle's diameter is twice its radius, we get the following equation: AB = 2 * radius = 2 * 360 = 720.

Now that we have the values, we can calculate:

2 * (156800) = AB2 => 2 * (156800) = 7202 => 313600 = 518400 - 2 * OA2 => OA2 = 102400 / 2 => OA = sqrt(51200) => OA = 40sqrt (2)

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(fo)(fog)(x) = 7x^(2)-6x+1

(gof)(x) = 7x^(2)+8x

Domain is a real number.

The first step in finding (fo)(fog)(x) and (gof)(x) is to substitute the functions into each other. For (fo)(fog)(x), we will substitute g(x) into f(x) for x:

(fog)(x) = f(g(x))

= f(7x^(2)-6x-1)

= (7x^(2)-6x-1) + 1

= 7x^(2)-6x

Now we will substitute (fog)(x) into f(x) for x:

(fo)(fog)(x) = f((fog)(x))

= f(7x^(2)-6x)

= (7x^(2)-6x) + 1

= 7x^(2)-6x+1

For (gof)(x), we will substitute f(x) into g(x) for x:

(gof)(x) = g(f(x))

= g(x+1) = 7(x+1)^(2)-6(x+1)-1

= 7x^(2)+14x+7-6x-6-1

= 7x^(2)+8x

The domain of each function is the set of all real numbers, since there are no restrictions on the values of x. Therefore, the domain of (fo)(fog)(x) and (gof)(x) is all real numbers.

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In interval notation, the solution of the inequality is (25, ∞).

To solve the inequality x(x-7) < x^2 - 5x - 50, we can rearrange the terms and factor the quadratic expression:
x^2 - 7x < x^2 - 5x - 50
-2x < -50
x > 25

In interval notation, the solution is (25, ∞).

So, the answer is (25, ∞).

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Answer:

60

Step-by-step explanation:

Answer:

The area of the triangle is 60 unit²

Step-by-step explanation:

We know that the area of a triangle is :

[tex]A= \frac{1}{2}(Base \times Height)[/tex]

Since Base = 12 unit and Height = 10 unit

So

[tex]A= \frac{1}{2}(12\times 10)=60\\[/tex]

Hence the area of this triangle is = 60 unit²

The percent increase in pipe footage sales is approximately 7%.

To find the percent increase in pipe footage sales, use the formula:

[(New Value - Old Value)/Old Value] × 100.

In this case, the new value is the amount of pipe sold in September (2,558 feet) and the old value is the amount of pipe sold in August (2,390 feet). Plugging these values into the formula, we get:

[(2,558 - 2,390)/2,390] × 100 = [168/2,390] × 100 = 0.0703 × 100 = 7.03%

Therefore, the correct answer is 7%, which is option A. The percent increase in pipe footage sales from August to September is 7%.

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The solution to the inequality is x <= 50. This means that any value of x less than or equal to 50 will satisfy the inequality.

To solve the inequality 100 - 3x >= -50, we want to find the values of x that satisfy this inequality.

Makayla solved the equation 100 - 3x = -50 and got x = 50. This equation is not the same as the inequality we want to solve, but we can check whether Makayla's solution is a valid solution to the inequality.

Substituting x = 50 into the inequality, we get:

100 - 3x >= -50

100 - 3(50) >= -50

100 - 150 >= -50

-50 >= -50

This is a true statement, so x = 50 is a valid solution to the inequality.

However, we also need to check whether there are any other values of x that satisfy the inequality. We can do this by rearranging the inequality to isolate x:

100 - 3x >= -50

100 + 50 >= 3x

150 >= 3x

50 >= x

Therefore, the solution to the inequality is calculated to x <= 50.

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The factored form is 2y(x - y) - 11x.

Factored form of a polynomial is when the polynomial is written as a product of its factors. Each factor is either a polynomial or a number. Factored form is useful for identifying the zeros of a polynomial and for solving polynomial equations.

To simplify the given expression, we need to combine like terms and factor if possible.

First, let's combine the like terms:

x^2 + 3xy - 4y^2 - 6x + 3y - x^2 - xy + 2y^2 - 5x - 3y

= 2xy - 2y^2 - 11x

Next, let's see if we can factor the expression:

2xy - 2y^2 - 11x

= 2y(x - y) - 11x

Since we cannot factor any further, the simplified expression in factored form is:

2y(x - y) - 11x

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Since the park is isosceles trapezoid-shaped, the two sides, AB and CD, that make up the parallel sides of the trapezoid are of equal length.

An isosceles triangle is a type of triangle with two sides of equal length. It has two equal angles opposite of the two equal sides, and the third angle is usually different. Isosceles triangles are named after the Greek term isoskelēs, which means “equal legs”. They are very common in geometry and are used in many applications, including architecture and engineering.

We can then use the midpoints of the adjacent sides of the trapezoid, E and F, to form a rhombus. Since the rhombus is formed from the midpoints of the two parallel sides, we know that the two sides AE and CF of the rhombus are of equal length. Similarly, the two sides BE and FD of the rhombus are also equal in length. This means that the trail, if constructed in the shape of the rhombus, will have all sides of equal length, satisfying the criteria set by the Parks Commission.

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