2(4x+3)=2(3x+7)+4x what does x =

Collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and

valina [46]

Answer:

21 windows

Step-by-step explanation:

collen family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?

Answer: Let the number of window Collen father would paint be a while that of her mother be b. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father a = 2b

Let the number of windows that would be needed to be painted each by Colleen and her 2 brothers be c because they would paint the equal number of windows.

The total number of windows to be painted = 2b + b + c + c + c = 3b + 3c = 3(b + c).

Collen painted 7 windows as her mother and her own share which is one less than the fathers share. Therefore b + c = 7.

Also the fathers share a = 2b = 7 + 1 = 8 windows. Therefore b = 4 which is the mother share

Therefore the total number of windows = 3(b + c) = 3(7) = 21 windows

3b + 3c = 21

3(4) + 3c = 21

12 + 3c = 21

3c = 21 - 12

3c = 9

c = 3 which is collen and her brothers share

6 0

3 years ago

Use the Fundamental Theorem for Line Integrals to find Z C y cos(xy)dx + (x cos(xy) − zeyz)dy − yeyzdz, where C is the curve giv

Harrizon [31]

Answer:

The Line integral is π/2.

Step-by-step explanation:

We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

$f_x = ycos(xy)$

$f_y = xcos(xy) - ze^{yz}$

$f_z = -ye^{yz}$

we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

$\int{ycos(xy)} \, dx = \int cos(u) \, du = sen(u) + C = sen(xy) + C(y,z)$

(Remember that c is treated like a constant just for the x-variable).

This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.

$\int {-ye^{yz}} \, dy = \int {-e^{u} \, dy} = -e^u +K = -e^{yz} + K(z)$

Where, again, the constant of integration depends on Z.

As a result,

$f(x,y,z) = cos(xy) - e^{yz} + K(z)$

if we derivate f over z, we obtain

$f_z(x,y,z) = -ye^{yz} + d/dz K(z)$

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.

3 0

3 years ago

Choose the inverse of y = x2 - 10x.

PilotLPTM [1.2K]

=Y2-10Y

We move all terms to the left:

-(Y2-10Y)=0

We add all the numbers together, and all the variables

-(+Y^2-10Y)=0

We get rid of parentheses

-Y^2+10Y=0

We add all the numbers together, and all the variables

-1Y^2+10Y=0

a = -1; b = 10; c = 0;

Δ = b2-4ac

Δ = 102-4·(-1)·0

Δ = 100

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

Y1=−b−Δ√2aY2=−b+Δ√2a

Δ‾‾√=100‾‾‾‾√=10

Y1=−b−Δ√2a=−(10)−102∗−1=−20−2=+10

Y2=−b+Δ√2a=−(10)+102∗−1=0−2=0

3 0

3 years ago

What’s the given m ABC = 70 and m ADC = 46

uysha [10]

Answer:

Step-by-step explanation:

Properties of a kite;

1). A kite has one pair of equal angles.

2). A kite has two pairs of adjacent sides.

3). Diagonals of a kite intersect at 90°.

4). Kite has at least one diagonal that bisects the opposite angles.

It's given in the question,

m∠ABC = 70° and m∠ADC = 46°

By the property number -4,

m∠2 = m∠3 = $\frac{70}{2}$ = 35°

m∠8 = m∠9 = $\frac{46}{2}$ = 23°

By the property number - 3,

m∠4 = 90°

By the property of interior angles in a triangle,

m∠3 + m∠4 + m∠5 = 180°

35° + 90° + m∠5 = 180°

125° + m∠5 = 180°

m∠5 = 55°

Similarly, m∠1 + m∠2 + 90° = 180°

m∠1 + 35° + 90° = 180°

m∠1 = 55°

Now m∠6 + 90° + m∠8 = 180°

m∠6 + 90° + 23° = 180°

m∠6 = 180 - 113 = 67°

Therefore, m∠6 = m∠7 = 67°

3 0

3 years ago

Select the table that represents a linear function. (Graph them if necessary.) O A. x 0 1 2 3 y 3 2 0 1 B. X 0 1 2 3 y 612 18 24

leonid [27]

Answer:

b because y moves same amount per x

7 0

3 years ago