Find the optimized volume of a rectangular prism with a surface area of 864 m^2

Answer:

x= 2

y= 7

z= 4

Step-by-step explanation:

Equation 1: x+y+z=13

Equation 2: x-z= -2

Equation 3: -2x+y=3

Add equation 2 and 1

(x+y+z)+(x-z)= 13 -2

2x+y= 11

Add this to equation 3

(-2x+y)+(2x+y)= 11+3

2y= 14

y= 7

Plug in y= 7 to equation 3

-2x+(7)= 3

-2x+7=3

-2x= -4

x= 2

Plug x=2 into equation 2

2-z= -2

4 = z

Answer:

D. -3,-2

Step-by-step explanation:

Let [tex]x^{2} +5x+6=0=(x+2)(x+3)\\[/tex], then  [tex]x+2=0[/tex] or [tex]x+3=0[/tex], thus [tex]x=-2[/tex] or [tex]x=-3[/tex]

Answer:

5.12

Step-by-step explanation:

5.021+.099 is the problem

we can ignore the 5 for now. .021+.099= .120

now we bring back the 5

5.120=5.12

Answer:

sorry this question is confusing

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

f(4) = 3(4²) - 2(4)

= 3(16) - 8

= 48 - 8

= 40

when x=4, f(x) = 40

Answer:

XY (height) is approximately 20.8 feet

Step-by-step explanation:

let h = XY

tan60° = h/12

h = 12·tan60°

h = 20.78 ft

Answer:

hey mate

the question is not understandable

Answer:

y = -8/3x + 33

Step-by-step explanation:

y2 - y1 / x2 - x1

9 - 1 / 9 -12

8 / -3

= -8/3

y = -8/3x + b

1 = -8/3(12) + b

1 = -32 + b

33 = b

b. 9.2

Step-by-step explanation:

cos(52) × 15 gives you the adjacent which is 9.2

Answer:

a, 20 side polygond b, the sum of the interior angles is 162°

Answer:

39 cents

Step-by-step explanation:

3.38÷8.5=0.39

Answer:

-3

Step-by-step explanation:

y1-y2/x1-x2 = slope

Plug in coordinates (-1,0) and (0,-3)

-3-0/0-(-1)

-3/1

-3

Answer:

-3

Step-by-step explanation:

Pick two points on the line

(-1,0) and (0,-3)

You can find the slope using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -3-0)/(0- -1)

    = (-3-0)/(0+1)

    = -3/1

    = -3

Answer:

2.03% Rate of Population Growth.

Step-by-step explanation:

According to the Question,

Given, In 2006 the population was 1148 and in 2014 the population was 1348.

2006⇒2014  (8 Years)

So, [tex]1148 * (1+\frac{x}{100} )^{8} = 1348[/tex]

[tex](1+\frac{x}{100} ) = \sqrt[8]{1.1742}[/tex]

(1 + x/100) = 1.0202

x/100 = 0.020276

x = 2.03% Rate of Population Growth

Answer:

The other exterior angles must be 145 degrees. There is only one answer because there cannot be 2 of 110 degree angles in a triangle, so the other two exterior angles must correspond to the 2 equal angles in the triangle.

Step-by-step explanation:

For an exterior angle, we know that an exterior angle added with its corresponding interior angle is equal to 180 degrees. Thus, 180 = 70 + i, or the interior angle. i is then 110 degrees.

An isosceles triangle has two equal angles. As a triangle can only be 180 degrees. we cannot have 2 of i, as doing so would be equal to 220 degrees. Therefore, for the other two interior angles, they must be equal. Representing o, their angles could be put into an equation of 110 + 2o = 180, so o = 35.

For the other exterior angles, their corresponding interior angles are equal to 35 each, so they must be 145 degrees. There is only one answer because there cannot be 2 of 110 degree angles in a triangle, so the other two exterior angles must correspond to the 2 equal angles in the triangle.

Answer:

192

Step-by-step explanation:

16^2+b^2= 20^2

256+b^2=400

b^2=144

b= 12

height = 12

1/2bh= Area of a triangle

12*32=384

384/2= 192

Answer:

DESCRIPTION: Large for a modern amphibian, the male California tiger salamander can reach up to 8.5 inches in length, the female up to seven. Adults have protruding eyes and long tails, and their slick bodies are mostly black with brilliant yellow spots and stripes on their back, sides, and tail. Larvae are greenish gray in color.

HABITAT: California tiger salamanders can be found in annual grasslands and oak woodlands with hot, dry summers and cool, rainy winters. For most of the year, they reside in underground burrows created and abandoned by small mammals. They need ephemeral pools for breeding.

RANGE: Historically these salamanders ranged throughout California's Sacramento and San Joaquin River valleys, the surrounding foothills, and the lower elevations of the state's central coast. Now their distribution is limited to disjunct vernal pool complexes in the northern part of their historical range. The northernmost and southernmost populations, residing in Sonoma and Santa Barbara counties respectively, are genetically distinct and geographically isolated from others.

MIGRATION: Once fall and winter rains begin, adult tiger salamanders emerge from underground hibernation habitat in mammal burrows and migrate to breeding ponds. After breeding, adults disperse back to uplands habitat to retreat underground. Adults may migrate long distances between summering and breeding sites: salamanders have been found along roads more than 1.2 miles from any known breeding ponds. Juvenile salamanders dispersing from ponds have been trapped more than 1,200 feet from their natal ponds.

BREEDING: Following early-winter rains, California tiger salamanders nocturnally emerge from their burrows and lay their eggs in newly formed vernal pools. After the eggs are fertilized internally, a female can lay up to 1,300, which she deposits individually or in small batches. Adults move back to their terrestrial burrows after breeding.

LIFE CYCLE: Within two weeks of egg fertilization, salamander larvae hatch, remaining in their natal pools for two to three months. By late spring or summer, once they reach metamorphosis, juveniles roam up to two miles away to hibernate in terrestrial habitat. Salamanders are thought to have lifespans of 10 years or more.

FEEDING: For the first six weeks of life, juveniles eat small crustaceans, algae, and mosquito larvae. Adult salamanders prey on aquatic insects, invertebrates, and tadpoles of Pacific tree frogs, California red-legged frogs, western toads, and spadefoot toads.

THREATS: The California tiger salamander is threatened by habitat destruction due to urban and agricultural development, habitat fragmentation, pesticides, hybridization with nonnative tiger salamanders, introduced diseases, and predation by nonnative species.

POPULATION TREND: Surveys showed that by 1993, the California tiger salamander had been extirpated from at least half of its historic localities. By 2004, only six tiger salamander meta-populations within 48 breeding ponds remained in Santa Barbara County, and by 2005, only seven viable tiger salamander breeding sites remained in Sonoma County.

Step-by-step explanation:

[tex]\begin{cases} h(x)=\sqrt{x}\\ g(x)=4x^2+4 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ g(\sqrt{a})=4(\sqrt{a})^2+4\implies g(\sqrt{a})=4\sqrt{a^2}+4\implies g(\sqrt{a})=\boxed{4a+4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(~~g(\sqrt{a})~~)\implies h\left( \boxed{4a+4} \right)=\sqrt{4a+4}\implies h(~~4a+4~~)=\sqrt{4(a+1)} \\\\\\ h(~~4a+4~~)=\sqrt{2^2(a+1)}\implies h(~~4a+4~~)=2\sqrt{a+1}[/tex]

Answer:

below

Step-by-step explanation:

that is the solution above

The simplest form of the given expression is [tex]\frac{1}{(x+1)(x-2)}[/tex].

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

Here, given expression;

 [tex]\frac{x+2}{4x^2+5x+1} X \frac{4x+1}{x^2-4}[/tex]

[tex]\frac{x+2}{4x^2+4x +x+1} X \frac{4x+1}{x^2-2^2}[/tex]

[tex]\frac{x+2}{4x(x+1)+1(x+1)} X \frac{4x+1}{(x+2)(x-2)}[/tex]

[tex]\frac{x+2}{(4x+1)(x+1)} X \frac{4x+1}{(x+2)(x-2)}[/tex]

[tex]\frac{1}{(x+1)(x-2)}[/tex]

Thus, the simplest form of the given expression is [tex]\frac{1}{(x+1)(x-2)}[/tex].

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Answer:

A. the first one

Step-by-step explanation:

The first one

Answer:

The money was invested at an interest of 14.28% per year.

Step-by-step explanation:

To determine at what percent rate of compound interest per year will the compound interest on $ 343000 be $ 169000 in 3 years, the following calculation must be performed:

343,000 x (1 + X / 1) ^ 3x1 = 343000 + 169000

343,000 x 1 + X ^ 3 = 512,000

1 + X ^ 3 = 512,000 / 343,000

1 + X ^ 3 = 1.4927

1 + 0.14286 ^ 3 = 1.4927

1.4927 = 1.4927

X = 0.14286 x 100 = 14.28%

Therefore, the money was invested at an interest of 14.28% per year.

The measure of ∠NPO is equivalent to 24°.

Given is that if the angle PON is equal to 132 degrees and the segment NP is bisector of the angle P and N.

Now -

OP = ON

So, this means that ∠OPN = ∠ONP = x° {say}

We can write -

∠OPN + ∠ONP + 132° = 180°

2x = 48°

x = 24°

Therefore, the measure of ∠NPO is equivalent to 24°.

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{

Question in English is as follows -

Determine the angle NPO, if the angle PON is equal to 132 degrees and the segment NP is bisector of the angle P and N.

Here's a hint, the correct answer is: 24 degrees.

}

Answer:

12

Step-by-step explanation:

The equation

2x(50) = 24

x(50) = 12

Answer:

y = 12

Step-by-step explanation:

36 - 24 = 12.

24 calories were burned in 100 minutes. 36 calories were burned in 150 minutes. That means that in 50 minutes (150 - 100) 12 calories were burned.

Answer:

[tex]8 - 5 = 3[/tex]

Step-by-step explanation:

Given

[tex]8 - 5 =[/tex]

Required

Solve

Step 1: Write as addition

Simply change the positions of -5 and (+)8

[tex]8 - 5 = -5 + 8[/tex]

Step 2: Add

[tex]8 - 5 = 3[/tex]

Answer:

1. -10 > x

2. No, because the more you raise the ticket price, the less people will attend.

3. C) -x - 6 > -3.5

4. you have to do yourself

Step-by-step explanation:

1. if you solve for 5 - 3x > 35 you get x < -30, which means that any answer will be less than -10

<2 and <6 -----> Neither

<1 and <4 ------> vertical

Hope it helps you...