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4 years ago

X + x + x + 2 ? Choose two answers

Mathematics

1 answer:

MA_775_DIABLO [31]4 years ago

4 0

Answer:

A and D

Step-by-step explanation:

$x + x + x + 2= 3 \times x + 2$

$= 3 x+ 2$

A is correct.

$x + x + x + 2 = 2x + 2 + x$

Factor out 2:

$2(x + 1) + x$

D is correct.

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Mary wants to buy a new house but needs money for the down payment. Her parents agree to lend her money at an annual rate of 2%,

lukranit [14]

Answer:

a) Simple interest paid = $360

b) Total repayment amount = $6360

Step-by-step explanation:

It is given that:

Principal, P = $6000

Rate of interest, R = 2%

Time, T = 3 years

(a) Total interest paid:

Formula for Simple Interest is given as:

$S.I. = \dfrac{P \times R \times T}{100}$

Putting the values of P, R and T to find out Simple Interest: $\\\Rightarrow S.I. = \dfrac{6000 \times 2 \times 3}{100}\\\Rightarrow S.I. = \$360$

(b) Total repayment amount:

We know that formula for total amount is given as:

Amount = Principal + Simple Interest

Amount = 6000 + 360 = $6360

So, total repayment amount = $6360

So, the answers are:

a) Simple interest paid = $360

b) Total repayment amount = $6360

3 0

4 years ago

In △ABC, AB = 13.2m,

luda_lava [24]

Answer:

(i) ∠ABH = 14.5°

(ii) The length of AH = 4.6 m

Step-by-step explanation:

To solve the problem, we will follow the steps below;

(i)Finding ∠ABH

first lets find <HBC

<BHC + <HBC + <BCH = 180° (Sum of interior angle in a polygon)

46° + <HBC + 90 = 180°

<HBC+ 136° = 180°

subtract 136 from both-side of the equation

<HBC+ 136° - 136° = 180° -136°

<HBC = 44°

lets find <ABC

To do that, we need to first find <BAC

Using the sine rule

$\frac{sin A}{a}$ = $\frac{sin C}{c}$

A = ?

a=6.9

C=90

c=13.2

$\frac{sin A}{6.9}$ = $\frac{sin 90}{13.2}$

sin A = 6.9 sin 90 /13.2

sinA = 0.522727

A = sin⁻¹ ( 0.522727)

A ≈ 31.5 °

<BAC = 31.5°

<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)

31.5° +<ABC + 90° = 180°

<ABC + 121.5° = 180°

subtract 121.5° from both-side of the equation

<ABC + 121.5° - 121.5° = 180° - 121.5°

<ABC = 58.5°

<ABH = <ABC - <HBC

=58.5° - 44°

=14.5°

∠ABH = 14.5°

(ii) Finding the length of AH

To find length AH, we need to first find ∠AHB

<AHB + <BHC = 180° ( angle on a straight line)

<AHB + 46° = 180°

subtract 46° from both-side of the equation

<AHB + 46°- 46° = 180° - 46°

<AHB = 134°

Using sine rule,

$\frac{sin 134}{13.2}$ = $\frac{sin 14.5}{AH}$

AH = 13.2 sin 14.5 / sin 134

AH≈4.6 m

length AH = 4.6 m

8 0

3 years ago

............................

Vika [28.1K]

Answer:

........

Step-by-step explanation:

you didnt give a proper question so i answed with ........

3 0

3 years ago

Read 2 more answers

If mBDE = 125 what is mGDF? A) 35. B) 45. C) 55. D) 65

joja [24]

A supplmentary angle = 180°

∠BDE and ∠BDF are vertical angles, and so are congruent.

∠BDF = 125°, because ∠BDF ≅ ∠BDE.

∠CDA ≅ ∠EDF

∠CDA = 90°

line BJ is angle bisector of ∠CDA. ∠CDB is 1/2 of ∠CDA

∠CDA = 90°

∠CDB = 90/2
∠CDB = 45°

∠GDF is a vertical angle of ∠CDB, and it's measurement will be the same as ∠CDB.

∠GDF ≅ ∠CDB
∠CDB = 45°
∠GDF = 45°

∠GDF = 45° should be your answer

hope this helps

7 0

4 years ago

Read 2 more answers

For the differential equations dydx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to thi

julsineya [31]

Answer:

1. (-4,6) there is no a solution to the equation through this point

2. (2,−6) there is no a solution to the equation through this point

3. (−5,39) there is a solution to the equation through this point

4. (−1,45) there is a solution to the equation through this point

Step-by-step explanation:

Using the existence and uniqueness theorem:

Let:

$F(x,y)=\sqrt{y^2-36} \\\\and\\\\\frac{\partial F}{\partial y} =\frac{y}{\sqrt{y^2-36} }$

Now, let's find the domain of $F(x,y)$ , due to the square root:

$y^2-36 \geq 0\\\\y^2\geq 36\\\\y \geq 6\hspace{12}or\hspace{12}y\leq-6$

So the domain of the function is:

$y \in R\hspace{12}y\geq6\hspace{12}or\hspace{12}y\leq-6$

Now, due to the fraction $\frac{\partial F}{\partial y}$ the denominator must be also different from 0, so:

$y^2-36\neq0\\\\y \neq \pm6$

So, the theorem tells us that for each $y_0\in R:\hspace{12}y_0>6\hspace{12}or\hspace{12}y_0$ there exists a unique solution defined in an open interval around $x_0$ .

1. (-4,6) there is no a solution to the equation through this point because $y_0=6$

2. (2,−6) there is no a solution to the equation through this point because

$y_0=-6$

3. (−5,39) there is a solution to the equation through this point because

$y_0>6$

4. (−1,45) there is a solution to the equation through this point because

$y_0>6$

6 0

4 years ago