All categories

3 years ago

1) Work out the value of x. 2) Give reasons for your answer. Please!

Mathematics

1 answer:

Stells [14]3 years ago

6 0

Answer:

x = 60

Step-by-step explanation:

Since the 3 sides of the triangle are congruent, then the triangle is equilateral with interior angles congruent and equal to 60°

x and the angle on the right of the triangle are alternate and congruent, so

x = 60

You might be interested in

You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the

Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0

3 years ago

Laura spent 4/3 of her savings on a new CD which equivalent fraction shows the amount Laura spent? 1/9, 2/8, 1/3, or 2/3

Sholpan [36]

Round 4/3 to the nearest half you should come up with 2/3

7 0

3 years ago

Triangle QRS has been rotated 90° to create triangle TVU. Using the image below, prove that lines RS and VU have the opposite an

Zanzabum

Answer:

If the line RS has been rotated 90 degrees, then VU will be perpendicular to RS and the two slopes must be opposite and reciprocal, i.e. product of the two slopes will equal -1.

As a verification, we find the locations of V and U from rotations of R & S.

(actually, the triangle had been rotated -90°, 90 ° clockwise)

Step-by-step explanation:

Slope RS, m1:

Slope VU, m2

Hence m1*m2=1*-1=-1, meaning that m1 and m2 are opposite (in sign) and are reciprocal to each other, as expected

6 0

3 years ago

Carlos needs 1.7 meters of wire for one project and 0.8 meters of wire for another project shade the model to represent the tota

vesna_86 [32]

Answer:

Step-by-step explanation:

Given that ;

Carlos needs 1.7 meters of wire for one project &

0.8 meters of wire for another project

we are to shade the model to represent the total amount of wire Carlos needs .

NOW;

For both projects ; Carlos needs ( 1.7 + 0.8) meters of wire = 2.5 meters of wire

In the attached files below. the first picture shows the diagram attached to the question and the second one shows the shading of the model which represent the total amount of wire Carlos needs.

7 0

3 years ago

How high is the building (ie. from what height was the potato launched) if h=-2(t-3)2+32

Llana [10]

Answer:

Step-by-step explanation:

To find the height from which the potato was launched, you need to set the time to 0 (since that is at the beginning). Plugging this into the equation, you get:

$h=-2(0-3)^2+32$

h=-2(9)+32

h=32-18

h=14

Hope this helps!

5 0

3 years ago