Find the exact length of the third side.

10

8

Answer:

AC = 20.5, CB = 14.5

Step-by-step explanation:

Let X be the distance of AC, and Y be the distance of CB. We can write 2 equations with the given information:

[tex]x=y+6\\x+y=35[/tex]

Now we have a system of equations that we can solve for both variables.

Solve by substitution:

[tex](y+6)+y=35\\2y+6=35\\2y=29\\y=14.5[/tex]

Then the next equation:

[tex]x=14.5+6\\x=20.5[/tex]

x = 20.5, y = 14.5

or

AC = 20.5, CB = 14.5

20.5 is 6 longer than 14.5, and they add up to 35cm, so this is our solution.

Answer:

It will cost her $33.46

Step-by-step explanation:

She drives 32miles per gallon

In 448miles, she will use: (448 × 1)/32

= 14gallons

If a gallon costs $2.39

Then 14gallons will cost, 14×2.39

= $33.46

Answer:

x + 2

--------

49

Step-by-step explanation:

that's the answer

Answer:

Approximately 12.25%

Step-by-step explanation:

The compound interest formula is:

Final balance = Principal * (1 + interest rate/number of times interest compounded per year)^(number of times interest compounded per year * years elapsed)

If we want our final balance to be twice our principal, our formula looks like:

[tex]2P = P * (1 + \frac{r}{1})^{1*6}[/tex]

We can divide our principal from both sides to get the following equation:

[tex]2 = (1 + \frac{r}{1})^{6}[/tex]

Since anything divided by 1 is itself, we can simplify a little further to:

[tex]2 = (1 + r)^{6}[/tex]

Now, we need to solve for r.  We can start by taking the sixth root of both sides.

[tex]\sqrt[6]{2} = 1 + r[/tex]

Then subtract 1 from both sides:

[tex]\sqrt[6]{2} -1 = r[/tex]

Finally, we can use a calculator to get a decimal approximation:

0.1225 ≅ r

Answer:

its multiplication 4 times 3 the product is 12

Step-by-step explanation:

Answer:

1) x = 55°

2) x = 30°

3) x = 68°

Step-by-step explanation:

In the given set of questions where it requires to find the unknown value of x to prove that v ||w:

The Consecutive Interior Angles Theorem states that for any given two parallel lines cut by a transversal, the measures of a pair of consecutive interior angles have a sum of 180°. Hence, the pair of consecutive interior angles are supplementary.

1.)  In the given diagram, the two consective interior angles are m ∠70° and m ∠ 2x°.  As defined by the Consecutive Interior Angles Theorem:

m ∠70° + m ∠ 2x° = 180°

Solve for x algebraically:

70° + 2x° =  180°

Subtract 70° from both sides:

70° - 70° + 2x° =  180° - 70°

2x° =  110°

Divide both sides by 2 to solve for x:

[tex]\LARGE\mathsf{\frac {2x^{\circ}}{2}\:=\:\frac{110^{\circ}}{2}}[/tex]

x = 55°

Verify whether the value for x is valid:

70° + 2x° =  180°

70° + 2(55)° =  180°

70° + 110° =  180°

180° =  180° (True statement).

2) In the given diagram, the two consective interior angles are m ∠2x° and m ∠ 4x°.  As defined by the Consecutive Interior Angles Theorem:

m ∠2x° + m ∠ 4x° = 180°

Solve for x algebraically:

2x° + 4x° =  180°

Add like terms:

6x° = 180°

Divide both sides by 6 to solve for x:

[tex]\LARGE\mathsf{\frac {6x^{\circ}}{6}\:=\:\frac{180^{\circ}}{6}}[/tex]

x = 30°

The Consecutive Interior Angles Theorem still applies in this question. The two consective interior angles are m ∠90° and m ∠ (x + 22)°.  As defined by the Consecutive Interior Angles Theorem:

m ∠90° + m ∠ (x + 22)° = 180°

Solve for x algebraically:

90° + x° + 22 =  180°

Combine like terms:

112° + x° = 180°

Subtract 112° from both sides to isolate x:

112° - 112° + x° = 180° - 112°

x = 68°

Verify whether the value for x is valid:

90° + x° + 22 =  180°

90° + 68° + 22 =  180°

180° =  180° (True statement).

Answer:

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items with a certain order.

Answer:

Permutations mean each of several possible ways in which a set or number of things can be ordered or arranged.

Step-by-step explanation:

[tex]\dfrac{\sin \alpha}{\cos \alpha + \sin \alpha} - \dfrac{\cos \alpha}{\cos \alpha - \sin \alpha}\\\\\\=\dfrac{\sin \alpha(\cos \alpha - \sin \alpha) - \cos \alpha(\cos \alpha + \sin \alpha)}{(\cos \alpha + \sin \alpha)(\cos \alpha -\sin \alpha)}\\\\\\=\dfrac{\sin \alpha \cos \alpha - \sin^2 \alpha - \cos^2 \alpha - \cos \alpha \sin \alpha}{\cos^2 \alpha - \sin^2 \alpha}\\\\\\=\dfrac{-(\sin^2 \alpha + \cos^2 \alpha)}{\cos 2 \alpha}\\\\\\=-\dfrac{1}{\cos 2 \alpha}\\[/tex]

[tex]=-\left(\dfrac{1}{\tfrac{1- \tan^2 \alpha}{1 + \tan^2 \alpha}} \right)~~~~~~~~~~~~~~~~~~; \left[\cos 2\theta = \dfrac{1 - \tan^2 \theta}{1+ \tan^2 \theta} \right]\\\\\\\ = -\left(\dfrac{1+ \tan^2 \alpha}{1- \tan^2 \alpha}\right)\\\\\\= \dfrac{1+\tan^2 \alpha}{\tan^2 \alpha -1}[/tex]

Answer:

60 goldfish

because there is a ratio of 2 gold fish to 3 Betta fish you can cross multiply with 2/5 and x/150 to find the number of goldfish. you can also check the answer because 60 goldfish would leave 90 Betta fish. the ratio of 60:90 can be simplified to a ratio of 2:3

$ (30-8p)

Step-by-step explanation:

3 DRINKS- 3P

MEDIUM- 2p

large- 3p

so plus 8 p

4, 8, 12, 20

10, 20

The least common multiple of 4 and 10

I hoped this helped. :)

Answer:

i just need point im so sorry only in Geomotry

Answer:

no

Step-by-step explanation:

to be perpendicular the second equation would have to be -x (the opposite of x)

these lines are parallel

Answer:

No, not perpendicular

Step-by-step explanation:

Compare the slopes of the two lines.  In each case the slope is 1.  Therefore the slopes are not negative reciprocals of one another, and the lines are NOT perpendicular.

Answer: $15.90/hr

Step-by-step explanation:

We need to add 6% to her $15/hr current pay.  This can be calculated with:

$15/hr *(1+0.06) = $15.90/hr

The "(1+0.06)" represents a) 1  the current salary, and b) the 6% raise.

Answer:

i cant read it

can u type so i can help?

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

This is an isosceles triangle.  Two angles (D and F) are equal because the sides opposite them are equal (or vice versa).

Thus, side DE = side EF, or

12x - 8 = 4x + 16

Combining like terms:  8x = 24

Thus, x = 24/8 = 3

x = 3

Step-by-step explanation:

[tex] \\ \frac{2}{3} \times 2 +3 \frac{1}{3} [/tex]

[tex] \\ = \frac{4}{3} + 3 \frac{1}{3} [/tex]

[tex] \\ = \frac{4}{3} + \frac{10}{3} [/tex]

[tex] \\ = \frac{4 + 10}{3} [/tex]

[tex] \\ = \frac{14}{3} [/tex]

[tex] \\ = 4\frac{2}{3} \: \: or \: \: 4.67[/tex]

Answer:the question is not there

Step-by-step explanation:

Answer:

A = 147°

B = 33°

Answer:

It is a ratio, which could mean yes and no, mattering which side of the ratio the number goes to.

Step-by-step explanation:

Answer:

yes because it is the same

Answer:

$343.75

Step-by-step explanation:

$5.50 × 125 = $687.50 ÷ 2 = $343.75

Answer:

$343.75

Step-by-step explanation:

Multiply 5.50 by 125 hours to get the amount of money she has earned. Then since she saved half of it divide that amount which is $687.50 by 2 to get $343.75

Answer:

y= -1, x=3

Step-by-step explanation:

2x+y=5

x-y =4

x= 4+y

Sub 1 into 3

2( 4+y ) 4y =5

8+2y +y =5

8+3y =5

3y =5-8

3y =-3

y=-3÷3

y = -1 #

Sub y = -1 into 3 equation

x=4+(-1)

x=3 #

Answer:

He divided by n instead of n-1.

It is sample data so we need to divide by n-1 not n.

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

400!

Step-by-step explanation:

Answer:

Step-by-step explanation: