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katen-ka-za [31]
3 years ago
15

a principal of 3400 is invested at 6.5% interest, compounded annually. how many years will it take to accumulate 8000$ or more i

n the account
Mathematics
1 answer:
nataly862011 [7]3 years ago
3 0

Answer:

It will take him 14 years to accumulate $8000 or more.

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The measures of 4 angles of a quadrilateral are 4 3 and 2. Find the fourth measure
Vsevolod [243]

Answer:

The final angle would be 351

Step-by-step explanation:

All quadrilaterals have interior angles that add up to 360. So to find the remaining angle, we have to subtract each of these numbers from 360.

360 - 4 - 3 - 2 = 351

6 0
3 years ago
1. Remember what we know about vertical angles and solve for x. (SHOW WORK)
marusya05 [52]

Answer:

Ans 1. x= 7

Ans 2.a.

\overline {AC} \cong \overline {JL} \\\textrm{is the additional information required to prove the triangles are congruent by SAS postulate}

Ans.2.b.

\overline {BC} \cong \overline {KL} \\\textrm{is the additional information required to prove the triangles are congruent by the HL theorem}

Step-by-step explanation:

Solution:

1.

Vertically opposite angles are equal.

\therefore (x+16) = (4x-5)\\\therefore (4x-x) = (16+5)\\\therefore (3x) = (21)\\\therefore x = 7

2.a.

proof for Δ BAC ≅ ΔKJL by SAS postulate.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

\overline{AC} \cong \overline{JL}\ \textrm{additional information require to prove the tangles are congruent by SAS postulate}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Side-Angle-Side postulate...PROVED}

2.b.

proof for Δ BAC ≅ ΔKJL by HL theorem.

InΔ BAC and Δ KJL

BA ≅  KJ               Given

∠ BAC ≅ ∠ KJL   {measure each angle is 90}

\overline{BC} \cong \overline{KL}\ \textrm{additional information require to prove the tangles are congruent by HL theorem}\\\therefore \triangle BAC \cong \triangle KJL\ \textrm{By Hypotenuse Leg Theorem......PROVED}

5 0
3 years ago
What is the difference? Complete the equation. -4 - 2 1/2
Lina20 [59]

Answer: - 6 1/2

Step-by-step explanation:

We should note that:

=-4 - 2 1/2

= -6 1/2

For example, let's assume you owe Bob $4 and then you owe Bill $2 1/2. To calculate the total amount owed, you would have $6 1/2.

5 0
3 years ago
Solve for y<br> 3x+2.75y=2(.625y+5)
chubhunter [2.5K]

3x+2.75y=2(0.625y+5)\\\\3x+2.75y=2(0.625y)+9(5)\\\\3x+2.75y=1.25y+45\ \ \ \ |-3x\\\\2.75y=1.25y+45-3x\ \ \ \ |-1.25y\\\\1.5y=45-3x\ \ \ \ \ |:1.5\\\\y=30-2x

6 0
3 years ago
Solve the initial value problem yy′+x=x2+y2‾‾‾‾‾‾‾√ with y(1)=8‾√. To solve this, we should use the substitution u= x^2+y^2 help
leva [86]

Looks like the equation is

yy'+x=\sqrt{x^2+y^2}

Substitute u(x)=x^2+y(x)^2, so that u'=2x+2yy'. Then the equation is the same as

\dfrac{u'-2x}2+x=\sqrt u\implies u'=2\sqrt u\implies\dfrac{\mathrm du}{2\sqrt u}=\mathrm dx

Integrate both sides to get

\sqrt u=C\implies\sqrt{x^2+y^2}=C

Given that y(1)=\sqrt8, we have

\sqrt{1^2+(\sqrt8)^2}=C\implies C=3

so the solution is

\sqrt{x^2+y^2}=3

7 0
3 years ago
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