The area of a rectangle is 342 square units. Its length measures 19 units. Find the
length of its diagonal. Round to the nearest tenth of a unit.
pen

Answer:

Use the Pythagorean Theorem to calculate the length of the sides of a right triangle. A TV cut in half on the diagonal is a right triangle.

a^2 + b^2 = c^2

a is the width of the TV

b is the height of the TV

c is the diagonal size of the TV

a is equal to the length of b plus 15, and c is equal to 75. If we out those values into the formula, we get this:

(b+15)^2 + (b)^2 = (75)^2

Factoring that out, we get:

(b)^2 + 225 + (b)^2 = 5625

Then..

2b^2 = 5625 - 225

2b^2 = 5400

b^2 = 5400/2

b^2 = 2700

b = ✓2700

b = 51.9615242271 (round it to an even 52)

Next, we know that a = b + 15, so a = 67.

Therefore, the width of the TV is 67 inches, the height is 52 inches, the diagonal is 75 inches, and you have a very strangely shaped television with a 1.288 (approximately 5:4) aspect ratio. Older “square” TVs mostly had a 1.33 (4:3) ratio, and new TVs are usually either 16:9 (1.77) or 21:9 (2.33). While it's not impossible that you have an old square TV with a 75 inch diagonal, it's pretty unlikely…

Step-by-step explanation:

Answer:

298.24 mph at an angle of 89 degrees

Step-by-step explanation:

[tex]v_p[/tex] = Velocity of plane = 300 mph at 50 degrees

[tex]v_j[/tex] = Velocity of jet stream = 200 mph at 160 degrees

The velocity of the plane in component form is

[tex]v_p=300\cos50^{\circ}\hat{i}+300\sin50^{\circ}\hat{j}[/tex]

The velocity of the jet stream in component form is

[tex]v_j=200\cos160^{\circ}\hat{i}+200\sin160^{\circ}\hat{j}[/tex]

Resultant velocity is given by

[tex]v=(300\cos50^{\circ}+200\cos160^{\circ})\hat{i}+(300\sin50^{\circ}+200\sin160^{\circ})\hat{j}\\\Rightarrow v=4.9\hat{i}+298.2\hat{j}[/tex]

Magnitude is given by

[tex]|v|=\sqrt{4.9^2+298.2^2}\\\Rightarrow |v|=298.24\ \text{mph}[/tex]

Angle is given by

[tex]\theta=\tan^{-1}\dfrac{298.2}{4.9}=89^{\circ}[/tex]

The velocity of the plane is 298.24 mph at an angle of 89 degrees.

Answer:

c=100 the angles in a hexagon =720 so subtract all the angles from 720. 720-155-80-115-160-110=100

Answer:

8.8

Step-by-step explanation:

Normally, to find the distance between two points, you would use the distance formula, but these two points have the same x-coordinate, meaning they will form a vertical line when connected. To find the length of a vertical line you find the distance between the y-coordinates, in this case -4.7 and 4.1. Finding the distance is the same as finding the absolute value of the difference:

|4.1 -(-4.7)|

|4.1 + 4.7|

|8.8|

8.8

Answer:

D) 83

Step-by-step explanation:

x+7=90

x= 83

Hope it's helpful...

Answer:

D

Step-by-step explanation:

The diagonals of a kite are at right angles to each other, then

x + 7 = 90 ( subtract 7 from both sides )

x = 83 → D

Answer:

1) A serious girl - Una chica seria/Una joven seria

2) The talented boy - El chico talentoso/El joven talentoso

3) An outgoing girl - Una chica extrovertida/Una joven extrovertida

4) The tasty ice cream - El helado delicioso/El helado sabroso

5) A funny book - Un libro divertido/Un libro entretenido

Step-by-step explanation:

Now, we present a possible set of solution, as there are solutions as many synonyms exist in Spanish. Then:

1) A serious girl - Una chica seria/Una joven seria

2) The talented boy - El chico talentoso/El joven talentoso

3) An outgoing girl - Una chica extrovertida/Una joven extrovertida

4) The tasty ice cream - El helado delicioso/El helado sabroso

5) A funny book - Un libro divertido/Un libro entretenido

Answer:

Volume = 1526.04 cubic units

Step-by-step explanation:

Formula for volume of a cone:

V = πr²h/3

If we use 3.14 for pi, we get 1526.04:

V = 3.14(9)^2(18)/3

V = 1526.04

Answer:

Product: 96

GCF: 4

LCM: 24

Product of the GCF and LCM: 96

Step-by-step explanation:

Now that we know what definitions are, we can solve this word problem.

12 × 8 = 96.

96 is the product.

To find the greatest common factor, we can list all of the factors for each number.

12: 1, 2, 3, 4, 6, 12

8: 1, 2, 4, 8

The largest factor both numbers have in common is 4.

Therefore, 4 is the greatest common factor.

To find the least common multiple, we can list the multiples of both numbers.

12: 12, 24, 36, 48, 60, 72, 84, 96

8: 8, 16, 24, 32, 40, 48, 56, 64

The smallest multiple both numbers have in common is 24.

Therefore, 24 is the least common multiple.

Lastly, we have to find the product of the GCF and the LCM.

The GCF is 4 and the LCM is 24.

4 × 24 = 96.

96 is the product.

Therefore, 96 is the product of the greatest common factor and the least common factor of 12 and 8.

Answer:

7

Step-by-step explanation:

49 ÷ 7 = 7

Square root is always dividing by a whole factor :)

Answer:

(7, - 5 ) and r = 2

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 7)² + (y + 5)² = 4 ← is in standard form

with centre = (h, k ) = (7, - 5 ) and r = [tex]\sqrt{4}[/tex] = 2

Answer:

g(x)=2x^2

Step-by-step explanation:

Multiplying by a constant will stretch the graph as shown. The graph of g(x) appears to pass through (1,2), so g(x)=2x^2 is a reasonable guess (I can't see the answer choices).

Answer:

Step-by-step explanation:

[tex]C=\pi D[/tex]

[tex]79.5=\pi D\\[/tex]

divide by [tex]\pi[/tex]

D = 25.30

radius = [tex]\frac{d}{2}[/tex]

[tex]\frac{25.30}{2} =12.65[/tex]

Answer:

r approx 12.7

d approx 25

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer: False, Quadratic can sometimes be solved by factoring. It can ALWAYS be solved using the quadratic formula.

Step-by-step explanation:

Hope this helps :)

Answer:

false

Step-by-step explanation:

I would like to ask you to go to the vet, or attempt to, as this might be a worm in the eye. The same thing happened to my dog.

Answer:

y = 15x - 19

Step-by-step explanation:

In order to pass through both (-2, 11) and (1, -34), then the equation must be y = 15x - 19. Hope this helps!

Given:

Length of escalator = 26 ft

Angle of depression = 41 degrees

To find:

The horizontal distance x the escalator covers to the nearest tenth of a foot.

Solution:

In a right angle triangle,

[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

Using this formula for the given triangle, we get

[tex]\cos 41^\circ=\dfrac{x}{26}[/tex]

[tex]26\cos 41^\circ=x[/tex]

[tex]26(0.7547)=x[/tex]

[tex]19.6222=x[/tex]

Round the value to the nearest tenth.

[tex]x\approx 19.6[/tex]

Therefore, the escalator covers 19.6 ft horizontally.

Answer:

y=  -3          

y = 4                        

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

Answer:

x = 28

Step-by-step explanation:

====================================================

Explanation:

We set up a cosine ratio, since we want to connect the adjacent and hypotenuse. Then we'll use the inverse cosine, which is also known as arccosine, to isolate the angle value.

This is what your steps could look like:

cos(angle) = adjacent/hypotenuse

cos(L) = LM/LN

cos(L) = 18/60

cos(L) = 0.3

L = arccos(0.3)

L = 72.542396876278 which is approximate

L = 72.54 degrees approximately

Make sure your calculator is in degree mode.

Answer: 3/5

Step-by-step explanation:

11/15-2/15=9/15

9/15 simplified is 3/5 :D have a nice day! hoped this helped!

Answer:

a) y(x) = (x + 2)^2 -2

b) minimum

c) (-2, -2)

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

• If a > 0 then vertex is minimum

• If a < 0 then vertex is maximum

Given

y = x² + 4x + 2

(a)

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

y = x² + 2(2)x + 4 - 4 + 2

y = (x + 2)² - 2

(b)

Since a = 1 > 0 then vertex is minimum

(c)

(h, k ) = (- 2, - 2 ) ← coordinates of vertex

Answer:

D, B

Step-by-step explanation:

Question 8.

The shaded area should be on or below the line [tex]y=\frac{5}{2}x-2[/tex] AND below but not on the line [tex]y=\frac{1}{2}x+2[/tex]

Question 9.

See the attached image.

Shade on or under the line [tex]y=\frac{1}{2}x-1[/tex] AND above but not on the line [tex]y=\frac{3}{2}x+1[/tex].

Answer:

0.08, 8 hundreths, 8 x 1/100

Step-by-step explanation:

The first digit before the decimal is a unit.

The first digit after the decimal point is called a tenth

The second digit after the decimal point is called hundreths

The third digit after the decimal point is called a thousandths

The 8 is the second digit after the decimal point.

Therefore the answer is eight hundreths or represented by the decimal form of 0.08

It is also 8 x 1/100 because if we multiply this we get 0.08