the williams 1/3 of their total monthly income for rent and 1/4 for food. what fraction is remains for other expenses each month?

If you differentiate each piece with respect to x, you'd get

    [tex]\frac{d}{dx}(x)\cdot y + x \cdot \frac{d}{dx}(y) + \frac{d}{dx}(2x)+\frac{d}{dx}(3x^2)=\frac{d}{dx}(4)[/tex]

which becomes

    [tex]1\cdot y + x \cdot \frac{dy}{dx} + 2+6x^1=0[/tex]

which is equivalent to B.

The answer is B.

Answer:

8.  TN = 22 units

9.  RT = √(165) units

Step-by-step explanation:

It appears that point T is the circumcenter of triangle MNP.

A circumcenter of a triangle is:

As a perpendicular bisector is a line that divides another line segment into two equal parts at a right angle, then:

As point T is the circumcenter, ΔMTN, ΔNTP and ΔMTP are isosceles triangles and MT, TP and TN are the radius of the circumcircle.

Therefore:

To find the length of TN, find the value of x by equating the given expressions for MP and TP:

[tex]\implies \sf MT = TP[/tex]

[tex]\implies 6x - 56 = 3x - 17[/tex]

[tex]\implies 3x = 39[/tex]

[tex]\implies x = 13[/tex]

Substitute the found value of x into the expression for TP:

[tex]\implies \textsf{TP} = 3(13) - 17[/tex]

[tex]\implies \textsf{TP} = 22[/tex]

Therefore, as TN = TP then TN = 22 units.

First find the value of x by equating the given expressions for TN and TP:

[tex]\implies \sf TN=TP[/tex]

[tex]\implies 4x-17=x+10[/tex]

[tex]\implies 3x=27[/tex]

[tex]\implies x=9[/tex]

Substitute the found value of x into the expression for TN:

[tex]\implies \textsf{TN} = 4(9) - 17[/tex]

[tex]\implies \textsf{TN} = 19[/tex]

As RT is the perpendicular bisector of MN, then ΔTRN is a right triangle where ∠TRN is 90°.

Given:

To calculate the length of RT, use Pythagoras Theorem:

[tex]\implies \sf RN^2+RT^2=TN^2[/tex]

[tex]\implies \sf RT=\sqrt{TN^2-RN^2}[/tex]

[tex]\implies \sf RT=\sqrt{19^2-14^2}[/tex]

[tex]\implies \sf RT=\sqrt{165}[/tex]

The value of a is 6 and b is 12.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

given:

a + b= 18.......(1)

a/b= 1/2

or, a= b/2......(2)

Put the value of a from equation (2) in (1) we get

b/2 + b= 18

3b/2 = 18

3b= 36

b= 36/3

b= 12

and, a= b/2 = 12/2 = 6

Learn more about Equation here:

https://brainly.com/question/29657992

#SPJ1

She has 1 61/152 pounds of apples left

Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing

In order to find how many pounds of apples she has left, subtract the apple she sold from the apple she begins with. That is:

Apple left = 35 1/2 - (35 1/2 * 1/2) - (35 1/2 *4/19) - (35 1/2 * 1/4 )

Apple left = 1 61/152

Learn more about fractions on:

brainly.com/question/11562149

#SPJ1

The total value of the loan with the quarterly compounded interest

is $117599.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded quarterly is,

A = P(1 + (r/4)/100)⁴ⁿ.

[tex]A = 50000(1 + 6.15/100)^{4\times\frac{43}{12}}[/tex].

[tex]A = 5000(1 + 0.0615)^{14.33}[/tex].

[tex]A = 5000(1.0615)^{14.33}[/tex].

[tex]A = 5000\times2.352[/tex].

A = $117,599.

learn more about compound interests here :

https://brainly.com/question/14295570

#SPJ1

The dimensions that will maximize the enclosed area are 125 meters by 250 meters

Represent the dimensions with x and y

So, we have the following equations

Perimeter = 4x + 2y = 1000

Area = 2xy

So, we have

2x + y = 500

This gives

y = 500 - 2x

So, we have

Area = 2x(500 - 2x)

Expand

Area = 1000x - 4x^2

Differentiate and set to 0

1000 - 8x = 0

So, we have

8x = 1000

Divide

x = 125

Recall that

y = 500 - 2x

y = 500 - 2 * 125

y = 250

Hence, the dimension is 125 by 250

Read more about area at

https://brainly.com/question/22972014

#SPJ1

Answer:

3a + 3b

Step-by-step explanation:

The distributive property of multiplication over addition is

a(b + c) = ab + ac

Here we have

3(a + b)

We apply the distributive property and get

3 × a + 3 × b

which simplifies to

3a + 3b

Answer:

1.) 55.3896

2.) 30.1754

Step-by-step explanation:

Follow steps in the image. (didn't know if you had to round, so i just left the numbers as they are.)

-Hope this helped

1 ]

Given:-

[tex] \: [/tex]

To Find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \rm{Area \: of \: circle = πr²} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{= 3.14×(4.2)²} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{=3.14× 17.64} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{\rm{ \red{= 55.3896}}}}[/tex]

———————————————————————

2]

Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \rm{Area \: of \: circle = \rm{\frac{(π×d²)}{4} } }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: = \rm{\frac{3.14×38.44}{4} }\\ \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ = \cancel\frac{120.7016}{4} }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{\rm{ \green{=30.1754}}}}[/tex]

[tex] \: [/tex]

hope it helps!:)

Answer:

4/3

Step-by-step explanation:

sorry if I'm wrong

4/3

rise over run so up is rise side is run 4/3

Answer:

A. -7

That's it

Answer:

600 cm²

Step-by-step explanation:

let x = length of a side of the cube

all sides are equal in a cube

Volume = x³ = 1000 cm³

x = ∛1000 = 10 cm

Area of 1 side = 10cm x 10cm = 100 cm²

There are 6 equal sides in a cube

SA = 6(100) =  600 cm²

Answer: Its point B, its closer to the vertices of 4.

Step-by-step explanation:

(7/2,1.87)

the distance between the points

(4,0)and (0,3)

would be:

√(3−0)2+(4−0)2=√9+16=√25=5

Answer: The real part of the complex number is 0.

Step-by-step explanation:

Complex numbers are always in the format: a + bi

On the given complex number, -i√5 , it is representing the "bi" part of the standard complex number expression.

We are looking for the real part. The real part is the real number. Since -i√5 doesn't show a real part, we can infer that its real part is 0.

If you rewrite the expression with 0 as the real number, it is equivalent to the principle of the original:

0 + -i√5

This concept is similar to the idea:

y = mx + b

if the equation said:

y = 3x

we know that b is 0, although its not stated. This principle is used in complex numbers.

Thank you.

The requried area of 3 of the pieces is 231 square feet. Option B is correct.

The area of a circle is the amount of space enclosed by the circle in a two-dimensional plane. It is given by the formula:

A = πr²

where "A" is the area of the circle, "r" is the radius of the circle, and "π" (pi) is a mathematical constant with an approximate value of 3.14159.

Here,
The area of a full circle with a radius of 14 feet is given by:

A = πr²

A = (22/7) × (14)²

A = (22/7) × 196

A = 616 square feet (rounded to the nearest whole number)

If the circle is cut into 8 equal pieces, each piece will have an area of:

616 ÷ 8 = 77 square feet

Therefore, 3 pieces will have an area of 3 × 77 = 231 square feet.

Thus, the requried area of 3 of the pieces is 231 square feet. Option B is correct.

Learn more about circles here:

https://brainly.com/question/29142813

#SPJ2

Answer:

A

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

given diameter = 14 then r = 14 ÷ 2 = 7

A = π × 7² = 49π m²

Answer:

49π

Step-by-step explanation:

area of circle=pie*radius²

and radius=diameter/2

therefore

r=14/2

=7m

Area =π*7²

Area=49π

Answer:

w ≥ 87/7

Step-by-step explanation:

Step 1: Subtract 63 from both sides.

7w+63−63≥150−63

7w≥87

Step 2: Divide both sides by 7.

7w/7  ≥  87/7

w ≥ 87/7

When x is 4, the output of the equation is greater.

The value for x that produces the same output in both the graph and the equation is equal to 6.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios, a straight line, and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.

By critically observing the graphs, we can reasonably infer and logically deduce that they would produce the same output (range) at the ordered pair (4, 6).

Read more on graphs here: brainly.com/question/4546414

#SPJ1

The equation can be used to solve for x is 90-52 = (12x - 10)°

Angle geometry is a branch of mathematics that deals with the study of angles and their properties in two-dimensional figures such as circles, triangles, and polygons.

In the diagram, since vertically opposite angles are equal. Thus, we can say:

∠UTW =  ∠VTZ

90 - 52 = (12x - 10)°

38 = 12x - 10

12x = 38 + 10

12x = 48

x = 48/12

x = 4

Therefore, the equation is 90-52 = (12x-10)°

Learn more about angle geometry on:

brainly.com/question/29399006

#SPJ1

The length of the side D'E' is 9 units for the given translated triangle D'E'F'.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

As we know that the translation does change the change location but it can't change the shape of the figure.

According to the given question, triangle DEF is translated as 6 units right and 6 units up.

This means there are no changes in the dimensions.

So D'E' =  DE

Thus, D'E' = 9 units

The length of the side D'E' is 9 units

To learn more about the transformations click here :

https://brainly.com/question/11352944

#SPJ1

answer = there are three photos. all answer in three photos

Answer:

y=3x+5

Step-by-step explanation:

qqqqqqqqqqqqqqqqssssssssss

9 miles for every ½ hour and 6 miles for every 20 minutes can be considered equivalent because they represent the same speed, just measured in different units.

To see this, we can convert the units to a common unit, such as miles per hour.

First, let's convert the 6 miles in 20 minutes to miles per hour:

[tex] \frac{6}{20} \times 60[/tex]= 18 miles/hour

Next, let's compare this speed to the 9 miles per ½ hour:

[tex] \frac{9}{ \frac{1}{2} } = \frac{9}{ \frac{1}{2} } \times \frac{1}{ \frac{1}{2} } = 18[/tex]

Since both speeds are equal to 18 miles per hour, we can conclude that they are equivalent. This means that the missing values are also equivalent.

To know more about the measurements and conversions visit :

https://brainly.com/question/28005036

#SPJ1

The sales price of the item is £18

From the question, we have the following parameters that can be used in our computation:

Discount = 1/3

Original price = 27

This means that

Sales price = original price * (1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Sales price = 27 * (1 - 1/3)

Evaluate

Sales price = 18

Hence, the sales price is #18

Read more about discount at

https://brainly.com/question/28383863

#SPJ1

The equations of the functions are

Function (a)

From the question, we have the following parameters that can be used in our computation:

x-intercepts = (4, 0) and (-2, 0)

This means that

y = a(x - 4)(x + 2)

Also, we have point (5, -7)

This means that

a(5 - 4)(5 + 2) = -7

So, we have

a =  -7

The equation becomes

y = -7(x - 4)(x + 2) --- in standard form

In vertex form, it is

y = -7(x - 1)^2 + 63

To test the point (2, 15), we have

y = -7(2 - 1)^2 + 63

Evaluate

y = 56 ---- false

Function (b)

From the question, we have the following parameters that can be used in our computation:

x-intercepts = (5, 0) and (-5, 0)

This means that

y = a(x - 5)(x + 5)

Also, we have point (-4, -36)

This means that

a(-4 - 5)(-4 + 5) = 36

So, we have

a =  4

The equation becomes

y = 4(x - 5)(x + 5) --- in standard form

In vertex form, it is

y = 4x^2 - 100

To test the point (3, -64), we have

y = 4 * 3^2 - 100

Evaluate

y = -64 ---- true

Read more about quadratic function at

https://brainly.com/question/1214333

#SPJ1

Answer:

(-1.5,-3.5)

Step-by-step explanation:

midpoint=(x1+x2)/2,(y1+y2)/2

-3+0/2, -2+( -5)/2

(-1.5,-3.5)

Answer:

ok one doll is 3 dollars and one purse is 6 dollars

and for the bottom I got 84 so I don't know I'm sorry

Step-by-step explanation:

Answer:

1. The unit price for a doll is three dollars. The unit price for a purse is six dollars.

2. One doll costs three. One purse costs six.

3. Polly spends $24 on the 2 dolls and 3 purses.

Step-by-step explanation:

Doing some calculations, 1 doll costs three dollars and 1 purse costs six dollars.

5 x 3 + 6 = 21

7 x 3 + 1  = 27

If Polly buys 2 dolls and 3 purses, that means she spends six dollars on the dolls and eighteen dollars on the purses.

(2 x 3) + (3 x 6) = $24

Polly spends $24 on 2 dolls and 3 purses.

As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

Demorgan's law can be utilised in set theory and boolean algebra to make mathematical formulations simpler. Let's say that the universal set U has two subsets, A and B. A' is A's complement, and B' is set B's complement.

Given that, (An B)' UC'.

Using the De Morgan's law we have:

(A ∩ B)’ = A’ ∪ B’.

Substituting this in (An B)' UC'. we have:

A’ ∪ B’ U C'

A' = {f, p, x, y}

B' = {f, g, h, p}

C' = {f, g, x, z}

A’ ∪ B’ U C'  = {f}

As sets A, B, and C are subsets of the universal set U, the value of A’ ∪ B’ U C'  = {f}.

Learn more about De Morgans law here:

https://brainly.com/question/13265106

#SPJ1