Two circles C₁ and C₂ have their centres at the point (3,4) and touch a third circle, C3.
The centre of C3 is at the point (0,0) and its radius is 2.
What is the sum of the radii of the two circles C₁ and C₂?

Answer:

Step-by-step explanation:

First of all it has to drop 15 degrees to get to 0.

We have another three degrees to go.

15 - - 3 = 18

The temperature change was 18 degrees from midnight to morning.

Yes, it is true that if "x" is an optimal solution to a linear programming problem, then it is a vertex of the feasible region.

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The multiplication of 6 × 43 by applying the distributive property of multiplication will be 258.

The general mathematical operation of multiplying two or more numbers to get a new multiplied number.

If both values are more than or less than one, the resultant multiplication will be greater or smaller than the numbers that will be multiplied.

For reference 4 × 3 = 12 and 4 × 0.5 = 2.

Given the multiplication,

6 × 43

⇒ 6 × (40 + 3)

By applying the distributive property of multiplication,

⇒ 6 × 40 + 6 × 3

⇒ 240 + 18

⇒ 258

Hence "The multiplication of 6 × 43 by applying the distributive property of multiplication will be 258.".

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He have to pay $3.25.

Let the number of miles traveled by a driver be x

The toll paid by the driver is then represented as y. (in dollar)

Linear equation : an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.

Since there is a linear relation between the two, we can assume the equation can be written as:

y = mx + c

From the given data, we get

0.24 = m(0) + c

c = 0.25

Using the second point:

1 = m(1) + 0.25

m = 1 − 0.25 = 0.75

Hence, the equation is y = 0.75x + 0.25.

If  x = 4, then:

y = 0.75 × 4 + 0.25

y = 5.50

Hence, He have to pay $3.25.

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Domain: (-∞, ∞)

Range: (-∞, ∞)

Domain and range help us describe the values a graph covers.

Defining Domain and Range

Remember that the x-values are along the horizontal axis, and the y-values are on the vertical axis.

The function given to us extends infinitely to the left and right as shown by the arrows. Additionally, the graph extends up and down infinitely; thus the range is also infinite.

Interval Notation

Interval notation should be written as (minimum value, maximum value). If the minimum and maximum values are included within the range or domain, then the parentheses should be replaced with brackets. This looks like [included minimum, included maximum]. Since a function cannot actually include infinity, an infinity symbol should never have brackets.

Eventually, this linear function will reach every single x and y-value in existence. So, both axes have a minimum of -∞ and a maximum of ∞. Thus, both the domain and range are (-∞, ∞).

Hint for future problems: all linear functions will have a domain and range of (-∞, ∞).

Equation are defined by equating two or more expressions. The solution to the system of equation is (k, (1+5k)/2)

System of equations are equations are equations that contains several variables and expression.

Given the system of equations

5x - 2y = -1

-15x + 6y = 3

Divide equation 2 through by -3 to have:

-15x/-3 + 6y/-3 = 3/-3

5x  - 2y = -1

You can see that both equations are equal. Let x = k so that;

5k - 2y = -1

-2y = -1 - 5k

2y = 1 + 5k

y = (1+5k)/2

Hence the solution to the system of equation is (k, (1+5k)/2)

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The polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.

Given the polynomials in the question;

-2x² + 5x - 3 and 5x² - 4

First, we find the sum of the polynomials

(-2x² + 5x - 3) + (5x² - 4)

-2x² + 5x - 3 + 5x² - 4

Collect like terms and simplify

-2x² + 5x² + 5x - 3 - 4

3x² + 5x - 7

Next, multiply the polynomial by 2.

2(3x² + 5x - 7)

Using distributive property,

2×3x² + 2×5x +2×-7

6x² + 10x - 14

Therefore, the polynomial is twice the sum of -2x² + 5x - 3 and 5x² - 4 is 6x² + 10x - 14.

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The coordinates of A'' will be ( -2, 5).

We are given that:

Quadrilateral ABCD is reflected across the x - axis.

We know that, when a refection is done about x-axis, the values of the abscissa x remain identical & the value of ordinate  just change their signs:

A(-5,-3) will become A'(-5,+3)

B(-6,-1) will become B'(-6,+1)

C(-3,-1) will become C'(-3,+1)

D(-2,-3) will become D'(-2,+3)

Now, the reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D".

So, the coordinates of A'' will become:

( - 5 + 3, 3 + 2)

( -2, 5)

Therefore, we get that, the coordinates of A'' will be ( -2, 5).

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Answer: 59,003

Step-by-step explanation:

8,429 x 7=

8,429 x (5+2)=

8,429 x 5 + 8,429 x 2=

4,214.5*10+16,858=                  ==> n*5=n/2 * 10

42,145+16,858=59,003

Answer:

3x^3-11y^2

Step-by-step explanation:

17x^3 -11y^2 -14x^3

collect like terms

17x^3 -14x^3 =3x^3

3x^3-11y^2

I hope it helps.

Answer:

I think it's 2(x+7).

Step-by-step explanation:

This is distributive function where a number is multiplied from outer value to inner parenthesis values.

I hope this is the right answer.

Step-by-step explanation:

so, this is a multiplication ?

6 3/4 × (-11.5)

let's bring the mixed numbers to full fractions, and then we can easily multiply.

6 3/4 = (6×4 + 3)/4 = (24 + 3)/4 = 27/4

-11.5 = -11 1/2 = (-11×2 - 1)/2 = (-22 - 1)/2 = -23/2

so, the multiplication is

27/4 × -23/2 = 27×-23 / 4×2 = -621/8 =

= (-616 - 5)/8 = (-77×8 - 5)/8 = -77 5/8

Answer:

-77 5/8

Step-by-step explanation:

6 3/4 can be turned into 6.75.

6.75 * -11.5 is -77.625

-77.625 can be simplified into 5/8

Brainliest pls?

The algebraic equation of the verbal statement is (x + 2) / 5 = 8 and the value of x is 38.

Algebraic Equation

An algebraic equation means the statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.

Given,

The quotient of two more than a number and five is eight.

Here we  need to translate the given verbal statement into an algebraic expression and solve it.

The quotient of two more than a number and five is eight.

Let, the number be x.

According to the question, the equation is

=> (x + 2) / 5 =8

=> x + 2 = 8 x 5

=> x + 2 = 40

=> x = 40 - 2

=> x = 38

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The solution of the simultaneous equations are x = 2, 3 and y = 3,9.

In mathematics; a set of simultaneous equations, also known as a system of equations or an equation system, it is a finite set of equations for which common solutions are sought.

WE have given simultaneous equations as;

y = x^2    ...(i)

y = x + 6  .....(ii)

Now Equating (i) and (ii) we get,

x^2 = x + 6

or, x^2 - x - 6 = 0

Then Solving we get;

x^2 - 3x - 2x - 6 = 0

x(x - 3) -2(x - 3) = 0

(x - 2)(x - 3) = 0

So, x = 2, 3

Now Putting x = 2, 3 in equation (i) we get;

y = 2^2

y = 4

and,

y = 3^2

y = 9

Thus, y = 3,9

Hence the solution of the simultaneous equations are x = 2, 3 and y = 3,9.

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Step-by-step explanation:

Solving steps

(2x-6)×(x-2)

Multiply

2x×x-2x×2-6x-6x 2

Calculate Multiply

2x²-4x-6x+12

Collect like terms

Solution

2x²- 10x + 12

Answer:

Final answer: P=(1,5)

Step-by-step explanation:

The line APB is a line such that AP/PB= 1/3. From the points A and B that we have we can find the distance between those points using the formula d= [(y2-y1)^2=(x2-x1)^2]^1/2

d= 4 (13)^(1/2)

Now the ratio is 1:3. AP= sq rt(13) and PB= 3 sq rt(13)

Using mid point formula the mid point of AB (say Q) = [(-1+7)/2,(2+14)/2]= (3,8).

Hence the mid point of AQ is P which can found out again using the mid point formula

P= [(-1+3)/2,(2+8)/2]= (1,5)

The price per yard of the ribbon is $6.69

First, we will need to convert  9 foot to yards as shown;

9 foot = 3 yards

This shows that a 3 yard piece of ribbon costs $20.07, the price per yard is expressed as;

Price per yard = 20.07/Total yard

Price per yard = 20.07/3

Price per yard = 6.69

Hence the price per yard of the ribbon is $6.69

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probability of picking a yellow ball: 10/20 (1/2)

probability of picking a red ball: 6/20 (3/10)

1/2 times 3/10 =

3/20

Answer:

41

Step-by-step explanation:

5y+x

Evaluate the expression

Let x=6 and y=7

5*7 +6

Multiply first

35 +6

Then add

41

Answer:

it 41

Step-by-step explanation:5(7)+6=41

Answer:

it 9/ 8

Step-by-step explanation:

2/4× 9/4

18/16

9/8

Answer:

31.5

Because if you Subtract 21 from 84 you get 63
then if you divide 63 by 2 you get 31.5 so your Answer would be 31.5.

The value of csc x=-13/5.

Given that the sin x=-5/13 and x∈[3π/2 , 2π).

A trigonometric function is a real function that relates the angle of a right triangle to the ratio of the lengths of the two sides. The basic functions are sin, cos, tan, cot, sec, csc.

The given function is sin x=-5/13.

As we all know that sin x=1/csc x or csc x=1/sin x.

As it is given that x∈[3π/2 , 2π) that means x lies in fourth quadrant and in fourth quadrant sin and csc is negative in it.

So, we will apply this identity csc x=1/sin x, we get

csc x=1/(-5/13)

csc x=-13/5

And it also lies in x∈[3π/2 , 2π).

Hence, the value of csc x when sin x=-5/13 and x∈[3π/2 , 2π) is csc x=-13/5.

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Answer:

6 miles per hour!

Step-by-step explanation:

A location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.

A prime meridian refers to an arbitrary meridian which is there in a geographic coordinate system. Here, the longitude is defined as 0°.

A prime meridian and its anti-meridian will together form a great circle in a geographic coordinate system.

The Equator is a circle of latitude, about 40,075 km in circumference, that divides Earth into the Northern and Southern hemispheres.

It is an imaginary line that is located at 0 degrees latitude, and is a halfway between the North and South poles.

Therefore, we get that a location that is 30 degrees north and 45 degrees west is west of the prime meridian and north of the equator.

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The value of the expression 91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ] is 47 by using PEMDAS.

We are given an expression as:

91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ]

By the PEMDAS rule, the expression will be:

= 91 - [ 22 {16 ÷ (39 + 9 - 40 ]

= 91 - [ 22 {16 ÷ (8) ]

= 91 - [ 22 {16 ÷ 8} ]

91 - [ 22 {2} ]

= 91 -[ 22 × 2 ]

= 91 - [ 44 ]

= 91 - 44

= 47

Therefore, the value of the expression 91 - [ 22 { 16 divided (39 + 3 of 3 - 40 )} ] is 47 by using PEMDAS.

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The weight average of the coordinates is 1

The given parameters are:

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

So, we have:

Weight average = (-2 * 3 + 5 * 1 + 6 * 1)/(3 + 1 + 1)

Evaluate the quotient

Weight average = 1

Hence, the weight average of the coordinates is 1

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Answer:

A: (-10, 2)

B: (-5, 2)

C: (-5, 7)

D: (-10, 7)

Step-by-step explanation:

When you reflect over the x axis, you flip the y value, so that what I did.

220/8 = 27.5

27.5 x 8 = 220

She’ll have to work 27 hours and 30 minutes to get 220 pounds.

The completed statement on the addition and subtraction operations with integers is presented as follows;

When the signs are of the integers of the same sign

1. Add the integers and copy the 2.) integer sign. When the signs are 3) different, subtract them and use the sign of the number with the greater 4) magnitude. If we add two same numbers with different signs, then the answer is equal to 5.) zero. The sum of two negative integer is a 6.) negative integer. The sum of two positive integers is a 7.) positive integer.

The process of adding integers is as follows;

Integers that have the same sign are added together, and the sign of the integers are placed before the result.

The addition of two integers that have different signs involve subtracting the integers and including the sign of the integer with the largest magnitude to the result.

The addition of two the same numbers that have different signs gives the same result as subtracting a number from itself, which is zero.

The sign of the result of the addition or subtraction of two integers of the same is the same as the sign of the integers in the operation.

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the exponential form of the complex number \[ e^{17\pi i/60} e^{27\pi i/60} e^{37\pi i /60} e^{47 \pi i /60} e^{57 \pi i/60}\]

= (2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]

[tex]e^1^7^\pi ^i/^6^0[/tex] + [tex]e^2^7^\pi^ i^/^6^0[/tex]+⋯+[tex]e^5^7^\pi ^i^/^6^0[/tex]

=[tex]e^1^7^\pi ^i^/^6^0[/tex](1+[tex]e^\pi^ i^/^6[/tex]+....+[tex]e^4^\pi ^i^/^6[/tex])

=[tex]e^1^7^\pi ^i^/^6^0[/tex] (1−[tex]e^5^\pi ^i^/^6[/tex]) ÷ (1−[tex]e^\pi ^i^/^6[/tex])

=[tex]e^1^7^\pi ^i/^6^0[/tex] ([tex]\frac{1}{2}[/tex](2+[tex]\sqrt{3}[/tex]) + [tex]\frac{1}{2}[/tex](3+2[tex]\sqrt{3}[/tex])i)

=(2+[tex]\sqrt{3}[/tex])e17πi/60(12+([tex]\sqrt{3}[/tex]/ [tex]2[/tex]) i )

=(2+[tex]\sqrt{3}[/tex])[tex]e^1^7^\pi ^i^/^6^0[/tex] [tex]e^\pi ^i^/^3[/tex]

=(2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]

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