What is the volume of the rectangular prism in the figure shown?

Answer:

2. 9

3.12 p^4 - 1/2 p^3 -8p^2 + 2p

Step-by-step explanation:

The degree of the polynomial is found by taking the number of the highest exponent.  We add the exponent when there is more than one variable in a term

5m^6n^3 =  degree (6+3)  = 9

3m^4n^2 = degree (4+2) = 6

So the polynomial is degree 9

Standard from is written from largest exponent to smallest exponent

12 p^4 - 1/2 p^3 -8p^2 + 2p

Answer:

105.35

Step-by-step explanation:

:)

Answer:

12 years will it take for light from the star to reach Earth.

Step-by-step explanation:

As per the given statement: A certain star is 1.135 × 10^14 km away from Earth. If light travels at 9.4607 × 10^12 km per year.

⇒Speed of light travel = [tex]9.4607 \times 10^{12}[/tex] km per year

and Distance of a certain star from the Earth = [tex]1.135 \times 10^{14}[/tex] km

To find how long will it take for light from the star to reach Earth.

Using Formula:

[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]

or

[tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]

Substitute the given values we have;;

[tex]\text{Time} = \frac{1.135 \times 10^{14}}{9.4607 \times 10^{12}}[/tex]

Simplify:

Time = 11.9969981 year ≈ 12 years

therefore, 12 years will it take for light from the star to reach Earth.

Answer: choices B, C, D and E

B) triangle RSP is similar to triangle ZXY

C) triangle SRP is similar to triangle XZY

D) triangle PSR is similar to triangle YXZ

E) triangle RPS is similar to triangle ZYX

In short, the answers is nearly everything but the first and last answer choice

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

For the first triangle, angle S is 54 degrees. In the other triangle, angle X is also 54 degrees. This means that the two angles correspond as they are equal to one another. The answer will have the letters S and X show up in the same position, whether that position is the first, second or third place of the three letter sequence.

Choice A is not one of the answers. RPS ~ XYZ is false because of what I mentioned above. We see that S is shown last in RPS while X is shown first in XYZ. The letters S and X do not correspond together, so we can cross choice A off the list.

Choice B is one of the answers because we have R corresponding to Z (first letters of each sequence RSP and ZXY; both are 41 degrees) and we have S correspond to X, and we have P correspond to Y (both the same measure as well)

Choice C is another answer for similar reasons as choice B. The only difference is that R and S have swapped, so have X and Z. The order is important or else things wouldn't line up properly.

Choice D is another answer. Again we have the same correspondence of P to Y (both in the first slot), S to X (second slot), and R to Z (third slot). For each slot, the pair of angles are both the same measure.

Choice E is another answer. Similar reasons as before, just a different order.

Choice F is not one of the answers. We see that P and Z occupy the second slots, but they aren't congruent angles.

Answer:

2,3,4,5 u-u welcome child

Step-by-step explanation:

Answer:

The senior's ticket cost is A, $5.

Step-by-step explanation:

say a children's ticket was $7; 7 + 7 + 14

so if an adult ticket is twice as much, let's say it was $10 per adult ticket.

one adult ticket plus two children's tickets would be $24 with these numbers.

two seniors ($5) + one children's ticket ($7) would be $17

therefore, we can conclude that a senior's ticket would cost $5

Answer:

15 students joined the radio-controlled model club

Step-by-step explanation:

The students joining the  radio-controlled model club were divided into three equal groups i.e

a) Radio-controlled boat group

b) Radio-controlled car group

c) Radio-controlled airplane group

10 new students joined the Radio-controlled airplane group  and the new sum of students in this group is 15.

This implies that there were 5 students in Radio-controlled airplane group  before the joining of 10 new students.

In the starting, the three groups have equal number of students which means that Radio-controlled boat group, Radio-controlled car group, Radio-controlled airplane group  have 5 students in each group. Thus, In the beginning there were total 15 students who joined the radio-controlled model club

The parametric equations that represent the sphere surface between the planes z=±6 are x = 12*sin(θ)*cos(φ), y = 12*sin(θ)*sin(φ), and z = 12*cos(θ), with θ and φ being between π/3 and 2π/3, and 0 and 2π respectively.

This question involves a mathematical concept known as parametric representation of a surface, specializing in spheres and planes. In a 3D coordinate system, the equation of a sphere is given by x² + y² + z² = r² where r is the radius of the sphere, but we restrict the z variable to lie in a certain range, which is between -6 and 6 in this situation.

To represent the sphere in parametric form, we often use spherical coordinates. The relationships between Cartesian coordinates and spherical coordinates are as follows: x = r*sin(θ)*cos(φ), y = r*sin(θ)*sin(φ), z = r*cos(θ). Here r = √144 =12, is the radius of the sphere.

Given the restrictions z = ±6, we have cos(θ) = ±6/12 = ±1/2, or θ = π/3 and 2π/3. So, the spherical coordinates range within 0 <= φ <= 2π and π/3 <= θ <= 2π/3.

This gives the parameters of the restricted surface in terms of θ and φ those are as follows: x = 12*sin(θ)*cos(φ), y = 12*sin(θ)*sin(φ), and z = 12*cos(θ).

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The parametric equations which represent the part of the sphere x² + y² + z² = 144 that lies between the planes z = -6 and z = 6 are: x = 12*sin(θ)*cos(Ď•), y = 12*sin(θ)*sin(Ď•), z = 12*cos(θ), with 60° ≤ θ ≤120° and 0° ≤ Ď• ≤ 360°.

The question asks for a parametric representation of part of a sphere lying between two planes. The given sphere equation is x² + y² + z² = 144, and the two planes are defined by z = -6 and z = 6. This is a common problem in multivariable calculus, and we solve it using spherical coordinates. In spherical coordinates, x= r*sin(θ)*cos(Ď•), y= r*sin(θ)*sin(Ď•) and z= r*cos(θ) where r is the radius, θ is the inclination angle, and Ď• is the azimuthal angle. For the given sphere, r = √144 = 12.

The bounds for z adds constraints to our inclination angle θ. Given -6 ≤ z ≤ 6, we determine corresponding bounds on θ. For z = r*cos(θ), we have -6 ≤ 12cos(θ) ≤ 6, or -1/2 ≤ cos(θ) ≤ 1/2. This yields θ values between 60° and 120°. The parametric equations describing the part of the sphere between the planes z = -6 and z = 6 are:

x = 12*sin(θ)*cos(Ď•)

y = 12*sin(θ)*sin(Ď•)

z = 12*cos(θ)

where 60° ≤ θ ≤120° and 0° ≤ Ď• ≤ 360°.

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Answer:

Triangle ABE is congruent to triangle CBD.

Step-by-step explanation:

Given two congruent triangles BAE and BCD where B is an apex of both triangles.

Given AB=BC, CD=AE, BE=BD

& also ∠AEB=∠BDC, ∠DCB=∠BAE, ∠ABE=∠CBD

By CPCT i.e. Corresponding parts of corresponding triangles

Correspondimg sides and angles area in the same position or spot in two different triangles.

Hence, Triangle ABE is congruent to triangle CBD.

Answer:

The correct answer option is 12.5 cm[tex]^2[/tex].

Step-by-step explanation:

We are given two triangles that are similar with one of the corresponding sides with known values.

The ratio of the corresponding sides of the smaller triangle to the larger triangle is [tex]\frac{16}{64} =\frac{1}{4}[/tex]. So the ratio between the areas of these triangles will be [tex]\frac{1}{4^2} =\frac{1}{16}[/tex].

If the area of the larger triangle is 200 cm[tex]^{2}[/tex] then the area of the smaller triangle will be = [tex]\frac{1}{16} *200=12.5[/tex].

Therefore, the area of the smaller triangle is 12.25 cm[tex]^2[/tex].

Formula to find Area of a triangle is

A=(height×base)/2

base of bigger triangle is=64cm^2

base of smaller triangle is=16cm^2

Area of bigger triangle is =200cmCm^2

area of smaller triangle=?

we imagine

height = base

then area of bigger trianglewillbe=64*64/2=2048

and area of smallertriangle will be=16*16/2==128

but we are given thatarea of bigger triangle is 200

when we  divide 2048/10

it approximately gives 200

similarly when we divide 128/10

it approximately gives 12.5cm^2

hence area of smaller triangle is 12.5cm^2

Answer:

A 0.2 L water was filled into the bottle from faucet each seconds.

Step-by-step explanation:

Unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or  6 miles per hour, they are called unit rates.

Given the statement: A 2 liter bottle is filled completely with water from a faucet in 10 seconds.

⇒ In 10 sec  a  2L bottle  is completely filled with water  from a faucet.

Unit rate per second =  [tex]\frac{2}{10} = \frac{1}{5} = 0.2 L[/tex]

Therefore, 0.2 L water was filled into the bottle each seconds.

Answer:

0.2

Step-by-step explanation:

Answer:

The function that represents the cost in cents of ‘d' dozen gumballs is y = 10d .

Step-by-step explanation:

As given

If 30 gumballs can be purchased for 3 dollars .

i.e

30 gumballs = $3

Now find out the cost of one  gumballs .

[tex]1\ gumballs = \$ \frac{3}{30}[/tex]

[tex]1\ gumballs = \$ \frac{1}{10}[/tex]

[tex]1\ gumballs = \$\ 0.1[/tex]

As 1 dollar = 100 cents

[tex]1\ gumballs = 0.1\times 100\ cents[/tex]

[tex]1\ gumballs = \frac{1\times 100}{10} \ cents[/tex]

1 gumballs = 10 cents

Thus the cost of one gumball is 10 cents .

As d = dozen gumballs.

Let us assume that the cost for ‘d' dozen gumballs = y

Than the function becomes

y = 10d

Therefore the  function that represents the cost in cents of ‘d' dozen gumballs is y = 10d .

In this problem, it is determined that Shelby can buy up to 11 small balloons and at least 3 large balloons with her $15 budget. Seven distinct combinations of small (x) and large (y) balloons are possible given the constraints x ≤ 11, y ≥ 3, and the total cost not exceeding $15.

Based on the information provided, we're dealing with inequalities and trying to determine how many small and large balloons Shelby can purchase with a budget of $15. Since Shelby needs at least 3 large balloons, we know y ≥ 3. Considering the remaining money for the small balloons, and given that small balloons cost $0.95, the maximum number (x) can be obtained by subtracting the cost for 3 large balloons from the total budget and dividing the remainder by the cost of a small balloon. Let's calculate it: $15 - $4.35 ($1.45 x 3 for large balloons) = $10.65. Then, $10.65 / $0.95 ≈ 11. Thus, x ≤ 11.

The outcome of the calculations thus suggests the possible pairs (x,y) for purchasing balloons are in such a way that Shelby can purchase up to 11 small balloons and needs at least 3 large balloons. Hence, 0.95x + 1.45y ≤ 15, with the constraints x ≤ 11 and y ≥ 3. Seven distinct combinations of small (x) and large (y) balloons are possible given these restrictions.

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Answer:

1) 3

2) {x = 9 or x = -1}

3) (b) The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]

Step-by-step explanation:

Problem 1

3 - 2 [tex]\frac{\sqrt{11} }{2} + \sqrt{11}[/tex]

i) Cancelling out the 2's from the top and bottom of the middle term, we get

3 - [tex]\sqrt{11} + \sqrt{11}[/tex]

ii) Cancelling out -[tex]\sqrt{11}[/tex] and +[tex]\sqrt{11}[/tex], we get

3 as the simplified form

Problem 2

x-1 = [tex]\sqrt{6x+10}[/tex]

Our first goal is to get rid off the radical on the right side

i) Squaring both sides, we get

[tex](x-1)^{2}[/tex]=[tex](\sqrt{6x+10})^{2}[/tex]

ii) (x-1)*(x-1) = 6x+10

iii) Applying the distributive property (a+b)(c+d) = ac+ad+bc+bd to the left side of the equation, we get

(x)(x)+(x)(-1)+(-1)(x)+(-1)(-1) = 6x+10

=> [tex]x^{2}[/tex]-x-x+1 = 6x+10

=> [tex]x^{2}[/tex]-2x+1 = 6x+10

iv) Subtract 6x from both sides, we get

[tex]x^{2}[/tex]-2x+1-6x = 6x+10-6x

v) Cancelling out 6x and -6x from the right side, we get

[tex]x^{2}[/tex]-2x-6x+1 = 10

=> [tex]x^{2}[/tex]-8x+1 = 10

vi) Subtracting 10 from both the sides, we get

[tex]x^{2}[/tex]-8x+1-10 = 10-10

vii) Cancelling out 10 and 10 from the right side, we have

[tex]x^{2}[/tex]-8x-10+1 = 0

=> 1[tex]x^{2}[/tex]-8x-9 = 0

viii) Coefficient of the first term = 1

Multiplying the coefficient of the first term and the last term, we get

1*(-9) = -9

We need to find out two such factors of -9 which when added should give the middle term -8

So, -9 and +1 are the two factors of -9 which when added gives us the middle term -8

ix) Rewriting the middle term, we get

[tex]x^{2}[/tex]-9x+x-9 = 0

x) Factoring out x from the first two terms and factoring out 1 from the last two terms, we get

x(x-9)+1(x-9)=0

xi) Factoring out x-9 from both the terms, we get

(x-9)(x+1)=0

xii) Either x-9=0 or x+1=0

xiii) Solving x-9=0, we get x=9

xiv) Solving x+1=0, we get x= -1

So, solution set {x = 9 or x = -1}

Problem 3

5 − 3i

a) In order to graph the complex number 5-3i, we need to move right by 5 units on the real axis and then move down by 3 units on the imaginary axis.

See figure attached

b) A complex number is in the form of z= a+ bi

i) Comparing 5-3i with a+bi, we get a=5 and b = -3

The modulus is given by

|z| = [tex]\sqrt{a^{2}+b^{2} }[/tex]

ii) Plugging in a=5 and b=-3, we get

|z| = [tex]\sqrt{5^{2}+(-3)^{2} }[/tex]  

iii) |z| = [tex]\sqrt{25+9} [/tex]

iv) |z| = [tex]\sqrt{34}[/tex]

The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]

Answer: No, we can't find a unique price for an apple and an orange.

Step-by-step explanation:

Since we have given that

Cost of 4 apples and 4 oranges = $10

Cost of 6 apples and 6 oranges = $12

We need to find the unique price for an apple and an orange.

According to question, our equations will be

[tex]4x+4y=\$10\\\\6x+6y=\$12[/tex]

since it is equation of parallel lines, as

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}\\\\\frac{4}{4}=\frac{6}{6}\neq \frac{10}{12}[/tex]

Hence, No, we can't find a unique price for an apple and an orange.

Answer:

d=1

Step-by-step explanation:

If North is i and South is -i

East is 1 and West is -1

The robot is facing East as it enters the maze, it will have a starting value of 1

Answer:

The value of d at the start of the maze will be 1 because 1 represents East .

Answer:

44

Step-by-step explanation:

8 * 5 1/2 =

8/1 * 11/2  =

88/2 =

44

Answer:

44

Step-by-step explanation:

HOPE THIS HELPS!

Answer: A. 4

The largest exponent in the polynomial tells us the max number of roots, x intercepts, or zeroes of the function. In this case, that happens to be 4. This is the degree of the polynomial. It is considered a quartic polynomial. It is also a trinomial since it has 3 terms (3x^4, x^2 and 1)

Answer:

ITs A

Step-by-step explanation:

The highest degree is 4 ( 3x^4)  so the maximum number of zeroes is 4.

Answer: b

Step-by-step explanation:

NOTE:

hypothesis : If two lines intersect at right angles

conclusion: then the two lines are perpendicular

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

P(tail) = [tex]\frac{1}{2}[/tex]

P(2) = [tex]\frac{1}{6}[/tex]

P(tail and 2 ) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

A. 8 rows.

B. 3 toy soldiers.

Step-by-step explanation:

We are told that Meliza has 43 toys soldiers, she line them up 5 to fight imaginary zombies .

A. Let us find the greatest multiple of 5 from 43.

Multiples of 5 are: 5,10, 15, 20, 25, 30, 35, 40, 45,..

We can see the greatest multiple of 5 from 43 is 40.

Let us divide 40 by 5 to find the number of rows that Meliza can make.

[tex]\text{Number of rows with 5 soldiers in each row}=\frac{40}{5}=8[/tex]

Therefore, Meliza can make 8 rows of 5 from 43 toy soldiers.

B. To find the number of soldier in last row we will subtract 40 from 43.

[tex]\text{Number of toy soldier in last row}=43-40=3[/tex]

Therefore, the number of toy soldiers in last row will be 3 soldiers.

Answer: Growth factor is 1.03 per year.

Correct option is C option.

Step-by-step explanation:

Given that water usage is increasing by 3% per year.

Time is measured in the years as given.

We need to find the growth factor for 3% increase per year.

We know a percent can be written decimal form by dividing by 100.

Therefore, 3% could be written as 3/100 = 0.03.

But the water usage would be increase by the factor of 1+0.03 that is 1.03.

Answer:

Blue

Step-by-step explanation:

2>0

Answer:

9,839 ft

Step-by-step explanation:

Answer: 2x + y

Step-by-step explanation:

logₐ(3) = x

logₐ(5) = y

logₐ(45) = logₐ(3²· 5)

             = logₐ(3)² + logₐ(5)

             = 2 logₐ(3) + logₐ(5)

             = 2     x      +   y        substituted given values (stated above)

Step-by-step explanation:

Here we make use of the laws of logarithms:

log_a(PQ) = log_a(P)+log_a(Q)

which implies the following corollary

log_a(P^2) = log_a(P)+log_a(P) = 2log_a(P)

Notice how the log of a product is reduced to the sum of the log of the factors.  (Advantage is taken of this fact in the use of logarithm tables before the wide-spread use of electronic calculators (pre-70's) )

So substituting

x=log_a(3)

y=log_a(5)

we have

log_a(45) = log_a(3^2 * 5) = log_a(3^2) + log_a(5)=2log_a(3)+log_a(5)

=2x+y

Answer:

X=3

Step-by-step explanation:

We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship.  This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.

The input value is [tex]\boxed{x =  3}.[/tex] Option (d) is correct.

Further explanation:

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

Given:

The options are as follows,

(a). [tex]x =  - 3[/tex]

(b). [tex]x = -1[/tex]

(c). [tex]x = 1[/tex]

(d). [tex]x = 3[/tex]

Explanation:

The functions are [tex]f\left( x \right){\text{ and }}g\left( x \right).[/tex]

It has been observed from the graph that the line of the functions [tex]f\left( x \right){\text{ and }}g\left( x \right)[/tex] intersects each other at [tex]x = 3.[/tex]

The input value is [tex]\boxed{x =  3}[/tex]. Option (d) is correct.

Option (a) is not correct.

Option (b) is not correct.

Option (d) is not correct.

Option (d) is correct.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Relation and Function

Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.

The answer is: 6,641.40$

Explanation:

Six thousand= 6,000

Six hundred= 600

Forty one= 41

Forty cents: .40

Now add all of these together:

6,000

+  600

+      41

+          0.40

Which will give you 6,641.40$

I hope this helps! :)

-LizzyIsTheQueen

Answer:

I would say your answer is $873.60

Step-by-step explanation:

$840.00

Tax (4%)

$33.60

Gross Amount (including tax)

$873.60

sorry if im wrong

Answer:

Points X and Y lie on more than one plane.

Step-by-step explanation:

From the  figure attached we have to find the points which lie on more than one plane.

M and R :

These are the points which lie on only one plane painted in yellow color.

A and S

These points lie on a plane perpendicular to the plane painted in yellow color.

X and Y :

These points lie on both the planes, painted in yellow color and the plane perpendicular to this.

M and S :

Point M lies on a plane in yellow color and point S lies on a plane perpendicular to the yellow plane.

Therefore, points X and Y lie on more than one plane.

Answer: [tex]\frac{2}{27}[/tex]

Step-by-step explanation:

blue = 8  , red = 6  , green = 4  , total = 18

red     and     green

 [tex]\frac{6}{18}[/tex]        x         [tex]\frac{4}{18}[/tex]

= [tex]\frac{1}{3}[/tex]         x         [tex]\frac{2}{9}[/tex]

= [tex]\frac{2}{27}[/tex]