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2 years ago

Simplify and solve each equation for the x

Mathematics

1 answer:

SpyIntel [72]2 years ago

8 0

Answer:

x = 2

Step-by-step explanation:

2(2x+1-x)=6

2(x+1)=6 add common factors

2x+2=6 distribute the 2

2x=4 subrtract 2 on both sides

x=2 divide 2 on both sides

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A survey in one middle school showed that 4 out of 9 students help cook meals at home. Predict how many out of the 720 students

valentinak56 [21]

Answer:

yes b

Step-by-step explanation:

yes

5 0

2 years ago

Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

2 years ago

Describe a situation that the expression -15÷(-15) can represent

FrozenT [24]

-15 so that is negative. so that is negative 15÷15 so 15 ÷15 is 1 so it would be -15÷-15=-1

7 0

2 years ago

I have a past due balance of $87.50 and my new charges are $75.00. I was also charged a late fee of 15% of my past due balance.

Kitty [74]

Past due balance = $87.50
Late fee = 15% of $87.50 = 0.15*87.50 = $13.125
New charges = $75.00

New total = 87.50 + 13.125 + 75 = $175.625

Answer: The new total is $175.63

8 0

2 years ago

Read 2 more answers

Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as

vesna_86 [32]

Answer:

1). System of equations- D + Q = 90 and D + 2.5Q = 175.50

2). There are 33 dimes and 57 quarters in the bank.

Step-by-step explanation:

Dylan has a bank that sorts coins as they are dropped in it.

A panel shows the total number of coins inside as well as the total value of these coins.

Let the number of dimes in the bank = D

and the number of quarters in the bank = Q

If the panel shows total number of coins = 90

Then the equation will be

D + Q = 90 -------(1)

And the panel displays the amount of the coins = $17.55

Then equation will be

0.10D + 0.25Q = 17.55 [1 Dime = $0.10 and 1 quarter = $0.25]

D + 2.5Q = 175.50 ------------(2)

Now we subtract equation (1) form equation (2)

D + 2.5Q - (D + Q) = 175.50 - 90

D + 2.5Q - D - Q = 85.5

1.5Q = 85.5

Q = $\frac{85.5}{1.5}$

= 57

By putting Q = 57 in the equation (1)

D + 57 = 90

D = 90 - 57 = 33

Therefore, there are 33 dimes and 57 quarters in the bank.

4 0

3 years ago