Mr. Barnes rode his bike twenty miles in three hours. Mrs. Barnes rode her bike twenty-four miles in four hours. Mr. Barnes was riding at a
rate than Mrs. Barnes.

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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In order for a number to be divisible by 12, it must be divisible by both 3 and 4.
To be divisible by 3, the sum of the digits must be divisible by 3.
7 + 7 + 3 + 1 + 8 + 6 + 2 + d + e = 34 + d + e

Since 34 is not divisible by 3, we need d + e to be a multiple of 3 in order for the sum to be divisible by 3.
Possible values for d + e are 3, 6, and 9.

To be divisible by 4, the last two digits of the number must be divisible by 4.
Therefore, we need de to be a multiple of 4.

Possible values for de are 12, 16, 32, 36, 52, 56, 72, 76, and 92.
Out of these, only 12, 36, 52, and 76 have a sum of digits that is a multiple of 3.

So the possible values for de are 12, 36, 52, and 76.
Therefore, the choices of the two-digit numbers de for which n is divisible by 12 are 12, 36, 52, and 76.

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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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Answer:

We can use the given formula to solve for the cost C:

P = R - C

We know that P = $49.32 and R = $81.18, so we can substitute these values into the formula:

$49.32 = $81.18 - C

Next, we can solve for C by isolating it on one side of the equation:

C = $81.18 - $49.32

C = $31.86

Therefore, it cost Zach $31.86 to make the jewelry he sold at the fair.

Answer:

The surface area of a right circular cylinder consists of three parts: the top and bottom circular faces, and the curved lateral surface.

The area of each circular face is given by the formula A = πr^2, where r is the radius. Therefore, the total area of the two circular faces is:

2A = 2πr^2

The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Therefore, the lateral surface area of the cylinder is:

A = 2πrh

Substituting the given values, we get:

A = 2π(5 cm)(9 cm)

Simplifying, we get:

A = 90π cm^2

Adding the areas of the circular faces and the lateral surface, we get the total surface area:

Total surface area = 2A + A = 3A

Substituting the value of A, we get:

Total surface area = 3(90π cm^2) = 270π cm^2

Therefore, the exact surface area of the cylinder is 270π square centimeters.

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

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!

Answer:

Step-by-step explanation:

4-5 would be less than 1 so it would be -1

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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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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Answer:

34

Step-by-step explanation:

3dds

Answer: Y=6/5

Step-by-step explanation:

Y=1/4X+6/5

(set X to zero 1/4(0) = 0)

Y=0+6/5

Y=6/5

The value of 8 cos(2x) accurate to 4 decimal places is -3.6009.

We can start by drawing a right triangle in Quadrant 1 with an angle x, where the opposite side is 13 and the adjacent side is 8.

Using the Pythagorean theorem, we can find the hypotenuse of the triangle:

 [tex]c^2 = a^2 + b^2\\ c^2 = 13^2 + 8^2\\ c^2 = 169 + 64\\ c^2 = 233\\ c = \sqrt{(233)}[/tex]

Now we can use trigonometric identities to find cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)[/tex]

We can find sin(x) using the triangle we drew earlier:

sin(x) = opposite / hypotenuse

sin(x) = 13 / [tex]\sqrt{(233)}[/tex]

And we can find cos(x) using the triangle as well:

cos(x) = adjacent / hypotenuse

cos(x) = 8 / [tex]\sqrt{(233)}[/tex]

Plugging these values into the identity for cos(2x):

[tex]cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (8 / \sqrt{(233))^2} - (13 /\sqrt{(233))^2} \\cos(2x) = (64 / 233) - (169 / 233)\\cos(2x) = -105 / 233[/tex]

Finally, we can find 8 cos(2x):

8 cos(2x) = 8 * (-105 / 233)

8 cos(2x) = -3.6009 (rounded to 4 decimal places)

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156 customers are expected to wear a black shoe.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

As per the given data:

Customers with black shoes = 13 out of 30

Customers with brown shoes = 17 out of 30

Total customers in the mall = 360

Probability that a customer wears black shoes:

P(B) = 13/30 = 0.433

Number of customers out of 360 expected to wear black shoes:

= P(B) × 360

= 0.433 × 360

= 156 customers.

Hence, 156 customers are expected to wear a black shoe.

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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:

Exact form: 121π

Decimal form: 380.1327111...

Step-by-step explanation:

The area of the circle is given by the formula A = πr², where A is the area of the circle and r is the radius.

Given the diameter of 22cm, we know that the radius is 11cm, as the radius is half the diameter.

We can then put this into the formula to find the area of the circle:

A = πr²

A = π * 11²

A = 121π

Note that the answer here is given in terms of π so it can be expressed in its exact form, as 121π is an irrational number roughly equivalent to 380.1327111... The answer you need to provide will depend on whether the question asks for the exact form, or to a certain number of decimal places / significant figures. If it the latter, you can round off the decimal answer as appropriate.

F = Fran's income

W = Winston's income

[tex]F+W=80000\hspace{5em}\stackrel{ \textit{one quarter} }{\cfrac{W}{4}}=\stackrel{ \textit{one sixth} }{\cfrac{F}{6}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{F+W=80000}\implies F=80000-W \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{W}{4}=\cfrac{F}{6}}\implies \stackrel{\textit{substituting from above}}{\cfrac{W}{4}=\cfrac{80000-W}{6}}\implies 6W=320000-4W \\\\\\ 10W=320000\implies W=\cfrac{320000}{10}\implies \boxed{W=32000}~\hfill \stackrel{ 80000~~ - ~~32000 }{\boxed{F=48000}}[/tex]

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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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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The requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

Given the functions f(x)=3x+5 and g(x)=1/(x−3), we can find the requested functions by applying the corresponding operations to the functions.

a. (f+g)(x) = f(x) + g(x) = (3x+5) + (1/(x−3)) = (3x(x−3)+5(x−3)+1)/(x−3) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = f(x) ∙ g(x) = (3x+5) ∙ (1/(x−3)) = (3x+5)/(x−3)

c. (2f+3g)(x) = 2f(x) + 3g(x) = 2(3x+5) + 3(1/(x−3)) = (6x+10+3/(x−3)) = (6x(x−3)+10(x−3)+3)/(x−3) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = 3g(x) - 4f(x) = 3(1/(x−3)) - 4(3x+5) = (3-4(3x+5)(x−3))/(x−3) = (-12x^2+8x+57)/(x−3)

Therefore, the requested functions are:

a. (f+g)(x) = (3x^2-4x-14)/(x−3)

b. (f∙g)(x) = (3x+5)/(x−3)

c. (2f+3g)(x) = (6x^2+7x-21)/(x−3)

d. (3g−4f)(x) = (-12x^2+8x+57)/(x−3)

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[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! :)

The matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]

To find a \( 2 \times 2 \) matrix \( A \) such that \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \], we can solve for A by multiplying both sides of the equation by the inverse of the left matrix. The inverse of \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] \] is \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right]. \] Multiplying both sides of the equation by this inverse gives \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right]A= \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right], \] which simplifies to \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \] Thus, the matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]

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Answer:

Well question is not clear rewrite

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!!!

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

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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Answer: 26

Step-by-step explanation:

65x40%

calculate 65x0.4

    Please give me brainliest

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