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3 years ago

What is the surface area of this triangular prism rounded to the nearest tenth?

Mathematics

1 answer:

alisha [4.7K]3 years ago

3 0

Answer:

43.638 cubic meters

Step-by-step explanation:

The triangular prism has 5 faces - 3 rectangular and 2 congruent triangular. Calculate the area of each face then add them together to find the surface area.

The triangles are 5.3 by 1.26 so the area of the two is 6.678.

The largest rectangle face is 5.3 by 3.3 so the area is 5.3*3.3 = 17.49.

The side rectangle face that is 3.3 by 3.6 so the area is 3.3*3.6 = 11.88.

The side rectangle face that is 2.3 by 3.3 so the area is 2.3*3.3 = 7.59.

Add all the areas together.

6.678 + 17.49 + 11.88 + 7.59 = 43. 638

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Kyle invests $11200 in two different accounts. The first account paid 10 %, the second account paid

Vedmedyk [2.9K]

Answer:

Kyle invested 5,800 at 10% and 5,400 at 7%.

Step-by-step explanation:

Let x be the amount Kyle invests in the 10% account.

0.1x + 0.07(11200 - x) = 958

0.1x + 784 - 0.07x = 958

0.03x = 174

x = 5800

4 0

3 years ago

4x – 3y=8 2. 5x – 2y = -11

AlladinOne [14]

Answer:

$x = -7$

$y = - 12$

Step-by-step explanation:

The given system is:

4x-3y=8

5x-2y=-11

We make x the subject in the top equation to get:

$x = \frac{3}{4}y + 2$

Plug this expression for x in the bottom equation to get

$5( \frac{3}{4}y + 2) - 2y= - 11$

We expand to obtain

$\frac{15}{4} y + 10 - 2y = - 11$

Multiply through by 4

$15y + 40 - 8y = - 44$

Group similar terms

$15y - 8y = - 44 - 40$

$7y = - 84$

$y = - \frac{84}{7} =-12$

This means

$x = -12\times \frac{3}{4} + 2$

$x = - 7$

6 0

3 years ago

What is the reason for Statement 3 of the two-column proof?

Ivenika [448]

Refer to the attached image.

Given:

The measure of $\angle JMK= 52^\circ$ and $\angle KML= 38^\circ$ .

Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove: $\angle JML$ is a right angle.

Proof:

Statements Reasons

1. $m \angle JMK=52^\circ$ Given

2. $m \angle KML=38^\circ$ Given

3. $m \angle JMK+m \angle KML=m \angle JML$

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. $52^\circ+38^\circ = m \angle JML$ Substitution property of equality

5. $90^\circ = m \angle JML$ Simplification

6. $\angle$ JML is a right angle. Definition of right angle

8 0

4 years ago

Please answer this now with correct answer

lana66690 [7]

Answer:

483.56 square milimeters

Step-by-step explanation:

In the above question, we obtain the following information:

Slant height = 15mm

Radius = 7mm

π = 3.14

Since we are given the slant height ,

the formula for surface area of a cone = πrl + πr²

= πr (l + r)

= 3.14 × 7(15 + 7)

= 3.14 × 7( 22)

= 21.98(22)

= 483.56 square milimeters

7 0

3 years ago

Solve this for Brainliest! See the attachment [Level - GCSE]

madreJ [45]

Answer:

$x = 3 + 4\sqrt{3}$

Step-by-step explanation:

OPQ is a right angle triangle.

Using Pythagoras

$x^{2} + (x+5)^{2} = (x+8)^{2}\\x^{2} + x^{2} + 10x +25 = x^{2} + 16x + 64\\x^{2} + x^{2} - x^{2} + 10x - 16x + 25 - 64 = 0\\x^{2} - 6x -39 = 0$

Using quadratic formula

$x = \frac{-b \± \sqrt{b^{2}-4ac}}{2a}\\x = \frac{-(-6) \± \sqrt{(-6)^{2}-4(1)(-39)}}{2(1)}\\x = \frac{6}{2} \± \frac{\sqrt{192}}{2}\\x = 3 \± \frac{8\sqrt{3}}{2}\\x = 3 \± 4\sqrt{3}$

$x = 3 + 4\sqrt{3} = 9.928(4s.f.)$

$x = 3 - 4\sqrt{3} = -3.928(4s.f.)$ (Length can't be negative)

∴ $x = 3 + 4\sqrt{3}$

3 0

2 years ago

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