Write the equation of the line passing through (-3,4) and perpendicular to -2x+7y=-3.​

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ1

Answer:

4

Step-by-step explanation:

Answer:2+2 = 4.............

Answer:

No, it will not be enough.

Step-by-step explanation:

Hello!

This estimation is incorrect, as 5.68 would round up to 6, and 4.1 would round down to 4.

Multiplying them both will give us 24, which can be justified as the actual product is 23.29.

Therefore the estimation of $20 will not be enough for 4.1 pounds of cherries.

The given exponential function equation is A = P(1+r)t, where P represents the principal amount, A represents the final amount, r represents the annual interest rate, and t represents the time in years.a.

The independent variable is t (time in years) while the dependent variable is A (final amount).b. The growth factor can be obtained by dividing A by P. Therefore, Growth factor = A/PLet us assume P=100, r=20%, and t=1. Then we can find A as follows:A = P(1+r)tA = 100(1+0.2)1A = 100(1.2)A = 120Therefore, the growth factor is:A/P = 120/100 = 1.2If we assume P=150, r=5%, and t=2, thenA = P(1+r)t = 150(1+0.05)2= 150(1.1025)= 165.375The growth factor is:A/P = 165.375/150 = 1.1025

Learn more about principal amount

https://brainly.com/question/30163719

#SPJ11

Use the Pythagorean theorem since you are working with a right triangle:

a^2+b^2=c^2a2+b2=c2

The legs are a and b and the hypotenuse is c. The hypotenuse is always opposite the 90° angle. Insert the appropriate values:

0.8^2+0.6^2=c^20.82+0.62=c2

Solve for c. Simplify the exponents (x^2=x*xx2=x∗x ):

0.64+0.36=c^20.64+0.36=c2

Add:

1=c^21=c2

Isolate c. Find the square root of both sides:

\begin{gathered}\sqrt{1}=\sqrt{c^2}\\\\\sqrt{1}=c\end{gathered}1=c21=c

Simplify \sqrt{1}1 . Any root of 1 is 1:

c=c= ±11 *

c=1,-1c=1,−1

Answer:

x=0

Step-by-step explanation:

4x+9-x-3x=9

4x-x-3x=9-9

0x=0

x=0

The number of pumpkins that are not ripe is 15 pumpkins.

The number of spectators that were happy that UK won is 20 spectators

A fraction is a digit that is not a whole number. A fraction has a numerator and a denominator. An example of a fraction is 5/9. 5 is the numerator and 9 is the denominator.

Number of pumpkins that are not ripe = fraction of pumpkins that are not ripe x number of pumpkins

Fraction of pumpkins that are not ripe = 1 - fraction of pumpkins that are ripe

1 - 3/4 = 1/4

Number of pumpkins that are not ripe = 1/4 x 60 = 15 pumpkins

Number of spectators that were happy that UK won = fraction of spectators that were happy that UK won x number of spectators

5/9 x 36 = 20 spectators

To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498

#SPJ1

x= 7/4 - 3/4          

you just have to subtract on variable and then put it on the other side, eventually you will have to divide it all by 4, which you can't do, so it ends up as a fraction:)                                        

To find the divergence of the vector field f = yj - xk / (y^2 + x^2)^(1/2), we can use the divergence operator, which is defined as the dot product of the gradient operator (∇) and the vector field f.

The gradient operator in Cartesian coordinates is given by ∇ = (∂/∂x)i + (∂/∂y)j + (∂/∂z)k, where i, j, and k are the unit vectors in the x, y, and z directions, respectively. Applying the divergence operator to the vector field f, we have:

div(f) = (∇ ⋅ f) = (∂/∂x)(y/(y^2 + x^2)^(1/2)) + (∂/∂y)(-x/(y^2 + x^2)^(1/2)) + (∂/∂z)(0). Since the vector field f is only defined in the x-y plane, the z-component is zero, and there is no dependence on z.

Taking the partial derivatives, we have:

∂/∂x (y/(y^2 + x^2)^(1/2)) = (y^2 - x^2)/(y^2 + x^2)^(3/2)

∂/∂y (-x/(y^2 + x^2)^(1/2)) = (-xy)/(y^2 + x^2)^(3/2)

Therefore, the divergence of f is given by:

div(f) = (∇ ⋅ f) = (y^2 - x^2)/(y^2 + x^2)^(3/2) + (-xy)/(y^2 + x^2)^(3/2)

Simplifying this expression, we have the divergence of f in terms of x and y.

Note that the divergence measures the net flow or the flux of the vector field through an infinitesimally small volume element. In this case, the divergence gives us information about how the vector field f spreads or converges around a point in the x-y plane.

Learn more about partial derivatives here: brainly.com/question/32234595

#SPJ11

Answer:

46

Step-by-step explanation:

length x width x height

7 x 5 x 3

Answer: surface area = 142

Volume = 105

* make sure to add labels (units^2, etc.)

Step-by-step explanation:

Area = length x height

Volume = length x width x height

The expression equivalent to given expression is -1/(4x²+9x+5).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 4/(4x+5) -1/(x+1)

Here, 4(x+1)-(4x+5)/(4x+5)(x+1)

= (4x+4-4x-5)/(4x²+5x+4x+5)

= -1/(4x²+9x+5)

Therefore, the expression equivalent to given expression is -1/(4x²+9x+5).

To learn more about an equivalent expression visit:

https://brainly.com/question/28170201.

#SPJ1

Answer:

(1,2)

Step-by-step explanation:

The solution is the point the two lines meet, at (1,3).  It is the only point that the value of x=1 will result is y = 3 for both lines.

The values of w typically vary, on average, from the mean of the distribution about 3.46.

The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

For a geometric(p = 0.25) distribution, the variance is computed here as:

Var(X) = (1 - p)/ p2 = (1 - 0.25) / 0.252 = 12

Therefore, the standard deviation is computed as:

= ✓(12) = 3.46 observations.

This is the standard deviation of the given distribution here.

Learn more about standard deviation on:

https://brainly.com/question/24298037

#SPJ1

Answer:

\(\sqrt{b^2+(c- a)^2}\)

Step-by-step explanation:

Replace values in the distance formula

x2= b

x1= 0

y2= c

y1= a

Answer:

x=4, y=-1

Step-by-step explanation:

x=3y +7. equation 1

3x+4y=8. equation 2

substitute equation 1 into equation 2

3 (3y +7)+4y =8

9y+21+4y=8

13y+ 21=8

13y=8-21

y=-13/13

y=-1

substitute the value of y into equation 1

x=3(-1)+7

x=-3+7

x=4

The general equation of a circle is (x-h)² + (y-k)² = r²

Where,

Here we are given the equation (x+4)² + (y+5)² = 64 and given this we are asked to find the diameter as well as the coordinates of the center.

Finding the center

If (h,k) = center, then the coordinates of the center are the given values of h and k but negative. This is because the values are being subtracted from x and y. (x-h)² + (y-k)² = r²

This means that, (x+4)² + (y+5)² = 64 is the same as saying (x-(-4))² + (y-(-5))² = 64 based off of the general equation of a circle.

Notice how the plugged in values are negative rather than positive.

In conclusion, we can say that the center is at (-4,-5) (see attached image below to check answer)

In the equation, 64 takes the place of r²

So r² = 64

Taking the square root of both sides we get r = 8

So the radius is 8.

To convert to diameter we multiply by 2

So diameter = 8 * 2 = 16

In conclusion, a circle with the equation (x+4)² + (y + 5)² = 64, has a center  at (-4,-5) and a diameter of 16

a. The perimeter of the first triangle is and the perimeter of the second triangle is

b. The difference between the perimeters is

c The perimeter of the triangles when x is 3 are

Perimeter is a math concept that measures the total length around the outside of a shape.

The perimeter of a triangle = a+b+c

1. 4x+2 + 7x+7 + x+3

= 4x+7x+ x +2+7+3

= 12x +12

Perimeter of the second triangle

= 2x-5+x+7+5x-4

= 2x+5x+x-5+7-4

= 8x-2

2. The difference of the perimeters

= 12x+12 -( 8x-2)

= 12x-8x +12+2

= 4x +14

3. when x is 3

The perimeter of the first triangle

= 12(3) +12

= 36+12

= 48 units

The perimeter of the second triangle

= 8(3)- 2

= 22 units

learn more about perimeter of rectangle from

https://brainly.com/question/24382052

#SPJ1

Answer:

k = 9

Step-by-step explanation:

Consider the pattern on the right side , that is

\(T_{k}\) = k(k + 2) + 1 = k² + 2k + 1

Equating

k² + 2k + 1 = 100 ( subtract 100 from both sides )

k² + 2k - 99 = 0 ← in standard form

(k + 11)(k - 9) = 0 ← in factored form

Equate each factor to zero and solve for k

k + 11 = 0 ⇒ k = - 11

k - 9 = 0 ⇒ k = 9

But k > 0 , then k = 9

According to the given statement the inequality is 313131c + 191919m ≤ 706706.

To represent the condition based on the number of employees, we can write the following inequality:

313131c + 191919m ≤ 706706

- Let c denote the number of cars and m denote the number of motorcycles.

- Since it takes 313131 employees to build a car and 191919 employees to build a motorcycle, we multiply the number of cars (c) by 313131 and the number of motorcycles (m) by 191919.

- The total number of employees used should be at most 706706 (as stated in the question).

The inequality 313131c + 191919m ≤ 706706 represents the condition based on the number of employees for Genghis Motors to spend more than \$84000 to build cars and motorcycles, using at most 706706 employees.

To know more about inequality visit;

https://brainly.com/question/20383699

#SPJ11

I do not agree. To find how fast Spotify is downloading songs, divide the number of songs already downloaded by how long the playlist has been downloading.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

For example, assume that you are downloading a playlist that has 100 songs. 80 songs have been downloaded in the past two hours. In order to determine the rate at which songs are downloaded, divide 80 by 2.

Speed = 80 / 2 = 40 songs per hour

To learn more about division, please check: https://brainly.com/question/13281206

#SPJ1

1 - According to the conjugate zeros theorem if a complex number is the root of a polynomial its conjugate is a root as well.

2 - So the conjugates of i, -7i would be

-i, 7i, so

-i , 7i would ALSO be roots of the polynomial according to the conjugates zeros theorem and those are the two roots we were missing.

The price of each pair of skates is given as follows:

$8.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

A skating rink charges a rate of $4, hence the intercept b is given as follows:

b = 4.

Hence:

y = mx + 4.

A family rents 2 pairs of skates and pays a total of $20, meaning that when x = 2, y = 20, then the slope m, representing the cost of each pair, is obtained as follows:

20 = 2m + 4

2m = 16

m = 16/2

m = 8.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

If the provided SHA hash value is different from the one I calculated, it indicates that there has been a modification or alteration in the data or the process used to calculate the hash.

This inconsistency raises concerns about data integrity and the authenticity of the information.

SHA (Secure Hash Algorithm) is a cryptographic hash function that generates a unique hash value for a given input. It is designed to be highly sensitive to any changes in the input data, meaning even a small alteration in the data will result in a completely different hash value. Therefore, if the provided SHA hash value differs from the one I calculated, it suggests that either the input data has been tampered with, or there is an error in the hash calculation process.

In such a situation, it is important to investigate the cause of the discrepancy and determine the source of the error. It could be due to accidental data corruption, intentional tampering, or an error in the hash calculation algorithm or implementation. Validating the integrity of the data becomes crucial to ensure the accuracy and trustworthiness of the information.

To resolve the issue, a comparison of the original and modified data should be conducted, and the hash calculation process should be carefully reviewed. It is also advisable to verify the integrity of the data through other means, such as using digital signatures or checksums, to detect any unauthorized modifications.

To know more about SHA (Secure Hash Algorithm) refer here:

https://brainly.com/question/13073367

#SPJ11

The zeros of polynomial function f(x) = x³ + 2x² -x - 2 are x = -2, x = 1 and x = -1

Here, we have been given polynomial function  f(x) = x³ + 2x² -x - 2

The definition of zeros of function states that zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.

To find the zeros of function f(x), we need to equate f(x) to zero then solve it for x.

⇒ f(x) = 0

⇒  x³ + 2x² -x - 2 = 0

⇒ x²(x + 2) -1(x + 2) = 0             ............(Seperate out like terms)

⇒ (x + 2)(x² - 1) = 0                     .............(factor out like terms)

⇒ (x + 2)(x + 1)(x - 1) = 0  

⇒ (x + 2) = 0   OR  (x + 1) = 0  OR  (x - 1) = 0  

Thus x = -2, x = 1 and x = -1 are zeros.              

Learn more about function here:

brainly.com/question/28193995

#SPJ4  

The complete question is:

What are the zeros of the polynomial function  f(x)= x³ + 2x² -x - 2?

Answer: 2²/₃ cups of raisins.

Step-by-step explanation:

Question wants to know the number of cups needed for 4 batches of oatmeal bars.

Each batch needs 2/3 cups of raisins to make.

If there are 4 batches to be made therefore, one must multiple the 2/3 cups to make one batch by 4 to find out the number needed to make 4 batches.

= 2/3 * 4

= 8/3

= 2²/₃ cups of raisins.

The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

a) The differential equation expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is suffering from Warfarin  is given a pill containing 2.5 mg of Warfarin then,

dQ/dt = -kQ
here Q(0) = 2.5

b) The differential equation the expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is not suffering from Warfarin  is given a pill containing 0.5 mg/hr then,

dQ/dt = -kQ + r
where Q(0) = 0
Here
k = rate constant
r = rate of administration
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

To learn more about differential equation,
https://brainly.com/question/1164377
#SPJ4

The rate at which Warfarin leaves the body should be proportional to the amount still in the body, not a constant rate of 2.5. So the correct differential equation for part (b) is:

Q' = 0.5 - kQ, where Q(0) = 0

Where k is the proportionality constant for the rate of elimination.

Explanation

(a) Let's denote the rate of elimination as k, where k > 0. Since the elimination rate is proportional to the amount of warfarin, we can write the differential equation as:

Q'(t) = -kQ(t)

Given that the initial condition is a 2.5 mg pill, the initial condition should be:

Q(0) = 2.5

So the differential equation for part (a) is:

Q'(t) = -kQ(t), Q(0) = 2.5

(b) In this case, the patient receives warfarin intravenously at a rate of 0.5 mg/hour. Thus, we should add the rate of administration to our equation:

Q'(t) = 0.5 - kQ(t)

The initial condition is still that the patient has no warfarin in her system:

Q(0) = 0

So the differential equation for part (b) is:

Q'(t) = 0.5 - kQ(t), Q(0) = 0

To learn more about differential equation : brainly.com/question/14620493

#SPJ11

Answer + Step-by-step explanation:

2x – y + 1 = 0

We know that the graph of a linear equation is a line.

So ,in order to draw it we need to find two points A and B of the line

Afterward, we join A and B to get the graph.

2x – y + 1 = 0

If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)

If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB

Now ,all we have to do is plotting A and B

on the coordinates plane ,then connecting then with a line.

According to the graph (check the attached image) :

If (h,4) ∈ line AB ⇒ h = 3/2

If (1/2 , k) ∈ line AB ⇒ k = 2

Answer:

3/8 or 0.375

Step-by-step explanation:

1/8 + 1/4

1/8+ 1*2/4*2

1/8+2/8

1+2/8

3/8

0.375