Find the lateral area and surface area of the following figure
Round to the nearest hundredth if necessary

Answer:

[tex]AC=5[/tex]

Step-by-step explanation:

From the question we are told that:

Dimensions

[tex]AD=4\\BD=6[/tex]

Generally the equation for these similar right triangle is mathematically given by

[tex]\frac{AC}{AB}=\frac{AB}{AD}=\frac{BC}{BD}[/tex]

[tex]\frac{AC}{AB}=\frac{AB}{AD}[/tex]

Where

[tex]AD=x[/tex]

[tex]AC=x+4[/tex]

Therefore

[tex]AB^2=x(x+4)[/tex]

Generally the Pythagoras equation for [tex]\triangle[/tex]ADB is mathematically given by

[tex]AB^2=BD^2+AD^2[/tex]

[tex]x(x+4)=4+x^2[/tex]

[tex]x(x+4)-(4+x^2)=0[/tex]

[tex]x^2+4x)-(4+x^2)=0[/tex]

[tex]4x-4=0[/tex]

[tex]x=1[/tex]

Therefore

[tex]AC=x+4[/tex]

[tex]AC=1+4[/tex]

[tex]AC=5[/tex]

Answer:

B. 68 square cm

Step-by-step explanation:

0.5 x 6 x 5 = 15

5 x 7 = 35

9 x 2 = 18

15+35+18 =68

Answer:

10.50

Step-by-step explanation:

16.50-6

Answer:

1.2 miles

Step-by-step explanation:

Morning laps = 3.5 laps

Evening laps = 1 lap

Total miles jogged = 5.4 miles

Total laps made = (3. 5 + 1) = 4.5 miles

Number of miles per laps covered :

Total miles jogged / number f lapses hugged around pond.

= 5.4 miles / 4.5

= 1.2 miles

Therefore, number of miles per round around the pond is 1.2 miles

Answer:

2

Step-by-step explanation:

y

Answer:

Lower and upper quartiles(B)

Step-by-step explanation:

Answer:

5.4332, 7.7, 7.03, and then 7.73

Answer: 5.4332, 7.7, 7.703, 7.73

Answer:

1.) Hypotenuse.

The hypotenuse is the longer side.

2.)Leg

Answer:

1.) Hypotenuse

2.) Leg

Step-by-step explanation:

The legs or bases of a triangle are the sides connected to the right angle.

The hypotenuse is the side across from the right angle and is always the longest side.

Answer:

30.52 feet.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The perimeter is the combined length of all the side lengths of a figure.

Answer:

a=0

b=-8

c=-16

d=0

e=-3

f=-6

Step-by-step explanation:

Answer:

Factored expression:  -15 (2x + 1)

Answer:

Its C

Step-by-step explanation:

Answer:

1: B

2: A

3: D

4: C

Step-by-step explanation:

In order to find the unit rate you have to divide the first number by the second number. You divide the first number because it is the gallons you are trying to find PER minute. In this case you are dealing with fractions which means you have to multiply the first number by the reciprocal of the second number.

Example 1:

3/4 ÷ 1/2

3/4 x 2/1

= 3/2

= 1 1/2

Example 2:

1 1/2 ÷ 1/2

3/2 ÷ 1/2

3/2 x 2/1

= 6/2

= 3

Answer:

It's 28

Step-by-step explanation

Answer:

(2,10) (4,20) (6,30) (8, 40)

Step-by-step explanation:

every minute, the pool fills up with 5 gallons.

if you look at the points, you will see a pattern

Answer: (x+3)^2+(y-4)^2=49

The answer is b :)

Step-by-step explanation:

Answer:

=6x−3

Step-by-step explanation:

Let's simplify step-by-step

4x+3(2x−1)−4x

Distribute:

=4x+(3)(2x)+(3)(−1)+−4x

=4x+6x+−3+−4x

Combine Like Terms:

=4x+6x+−3+−4x

=(4x+6x+−4x)+(−3)

=6x+−3

Answer:

6x - 3

Step-by-step explanation:

4x + 3(2x - 1) - 4x

Distribute, multiply every term inside the parenthesis by the term outside of it,

4x + (3)(2x) + (3)(-1) - 4x

Simplify,

4x + 6x - 3 - 4x

Simplify further, combine like terms,

6x - 3

Answer:

2268

Step-by-step explanation:

Answer:

QR ≈ 5.7 ft

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{QS}{QR}[/tex] = [tex]\frac{5}{QR}[/tex] ( multiply both sides by QR

QR × cos29° = 5 ( divide both sides by cos29° )

QR = [tex]\frac{5}{cos29}[/tex] ≈ 5.7 ( to the nearest tenth )

Answer:

B) 16x² - 40x + 25

Step-by-step explanation:

1) Use square differences: (a - b)² = a² - 2ab + b².

[tex](4x)^{2} - 2 \times 4x \times 5 + {5}^{2} [/tex]

2)Use Multiplication Distributive Property: (xy)^a = x^a y^a.

[tex] {4}^{2} {x}^{2} - 2 \times 4x \times 5 + {5}^{2} [/tex]

3) Simplify 4² to 16.

[tex]16 {x}^{2} - 2 \times 4x \times 5 + {5}^{2} [/tex]

4) Simplify 5² to 25.

[tex]16 {x}^{2} - 2 \times 4x \times 5 + 25[/tex]

5) Simplify 2 × 4x × 5 to 40x.

[tex] {16x}^{2} - 40x + 25[/tex]

Thus, the Anwer is Option B) 16x² - 40x + 25 .

Answer:

it would 13

Step-by-step explanation:

19-6=13 there you go

Answer:

[tex]\left[\begin{array}{ccc}1&2\\6&7\end{array}\right]\cdot \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}0\\-10\end{array}\right][/tex]

Step-by-step explanation:

The system of equation in matrix form is defined by following vector formula:

[tex]\vec A \cdot \vec x = \vec b[/tex] (1)

Where:

[tex]\vec A[/tex] - Matrix of coefficients.

[tex]\vec x[/tex] - Column vector of variables.

[tex]\vec b[/tex] - Column vector of results.

If we know that [tex]x + 2\cdot y = 0[/tex] and [tex]6\cdot x + 7\cdot y = -10[/tex], then the system of equations in matrix form is:

[tex]\vec A = \left[\begin{array}{ccc}1&2\\6&7\end{array}\right][/tex], [tex]\vec x = \left[\begin{array}{ccc}x\\y\end{array}\right][/tex], [tex]\vec b = \left[\begin{array}{ccc}0\\-10\end{array}\right][/tex]

Then,

[tex]\left[\begin{array}{ccc}1&2\\6&7\end{array}\right]\cdot \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}0\\-10\end{array}\right][/tex]