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1 year ago

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Bryan’s golf coach suggested he take some golf lessons. The Pro at Windy Fairways charges $20.00 per month plus $10.00 per lesso

n. The Pro at Sunny Sands charges $100.00 per month for unlimited classes. How many classes does he have to take for both Pro’s be the same price?

1 answer:

Aneli [31]1 year ago

5 0

Bryan has to take 8 classes for both Pro's to be the same price.

Step-by-step explanation:

Given,

Monthly charges of Pro at Windy = $20.00

Charges per lesson = $10.00

Let,

x be the number of lessons

W(x) = 10x +20

Monthly charges of Sunny Sands = $100.00

They offer unlimited classes.

S(x) = 100

For the price to be same;

W(x) = S(x)

$10x+20=100\\10x=100-20\\10x=80$

Dividing both sides by 10

$\frac{10x}{10}=\frac{80}{10}\\x=8$

Bryan has to take 8 classes for both Pro's to be the same price.

Keywords: function, division

Learn more about division at:

#LearnwithBrainly

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Evaluate the expression. * Captionless Image

raketka [301]

Answer:

An image without anything to explain it

Step-by-step explanation:

6 0

1 year ago

You invested a total of $12,000 at 4.5 percent and 5 percent simple interest. During one year, the two accounts earned $570. How

Luda [366]

Answer: You invested $6000 in both accounts.

Step-by-step explanation:

Let x represent the amount invested in the account earning 4.5% interest.

Let y represent the amount invested in the account earning 5% interest.

You invested a total of $12,000 at 4.5 percent and 5 percent simple interest. This means that

x + y = 12000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

Considering the account earning 4.5%

I = (x × 4.5 × 1)/100 = 0.045x

Considering the account earning 5%

I = (y × 5 × 1)/100 = 0.05y

During one year, the two accounts earned $570. . This means that

0.045x + 0.05y = 570 - - - - - - - - - - 1

Substituting x = 12000 - y into equation 1, it becomes

0.045(12000 - y) + 0.05y = 570

540 - 0.045y + 0.05y = 570

- 0.045y + 0.05y = 570 - 540

0.005y = 30

y = 30/0.005 = 6000

x = 12000 - y = 12000 - 6000

x = $6000

6 0

2 years ago

Figure ABCD is transformed to obtain figure A'B'C'D': A coordinate grid is shown from negative 6 to 6 on both axes at increments

nika2105 [10]

Given:

Vertices of ABCD are A(-4,4), (-2,2), C(-2,-1) and D(-4,1).

Vertices of A'B'C'D' are A'(3,-4), B'(5,-2), C'(5,1) and D'(3,-1).

To find:

The sequence of transformations that changes figure ABCD to figure A'B'C'D'.

Solution:

Part A:

The figure ABCD reflected across the x-axis, then

$(x,y)\to (x,-y)$

Using this rule, we get

$A(-4,4)\to A_1(-4,-4)$

Similarly, the other points are $B_1(-2,-2),C_1(-2,1),D_1(-4,-1)$ .

Then figure translated 7 units right to get A'B'C'D'.

$(x,y)\to (x+7,y)$

$A_1(-4,-4)\to A'(-4+7,-4)=A'(3,-4)$

Similarly, the other points are $B'(5,-2), C'(5,1),D'(3,-1)$ .

Therefore, the figure ABCD reflected across the x-axis and then translated 7 units right to get A'B'C'D'.

Part B:

Reflection and translation are rigid transformation, it means shape and size of figures remains same after reflection and translation.

Therefore, the two figures congruent.

8 0

2 years ago

F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0

1 year ago

A torch and a battery cost £2.50 altogether. The torch costs £2.00 more than the battery.

Genrish500 [490]

Answer:

$\frac{1}{10}$

Step-by-step explanation:

Let $t$ represent the cost of the torch and $b$ represent the cost of the battery.

The torch and a battery cost £2.50 altogether.

$\Rightarrow t+b=2.50$

The torch costs £2.00 more than the battery.

$\Rightarrow t=b+2.00$

We substitute the second equation into the first equation to get;

$\Rightarrow b+2.00+b=2.50$

$\Rightarrow 2b=2.50-2.00$

£2.50

$\Rightarrow 2b=0.50$

$\Rightarrow b=0.25$

The price of the battery is £0.25

We express this as a fraction of the total cost which is £2.50 to get;

$\frac{0.25}{2.5}=\frac{1}{10}$

8 0

2 years ago