21a5b³-14a³b² +63a²b
———————————-
7ab

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

Given that

The Triangle legs are 3 and 4 feet long, the hypotenuse is 5 feet long, and the prism height is 8 feet tall.

We have to determine the surface area and volume of each triangular prism

here a = 3ft b = 4ft  c = 5ft and height  h = 8ft

Surface area of triangular prism = ab + h(a+b+c)

= 3x4 + 8(3+4+5)

= 12 + 8(12)

= 12 + 96

= 108cm2

Volume of triangular prism = ½(abh)

= ½ (3x4x8)

=1/2(96)

= 96/2

= 48cm3

Therefore

The surface area of a triangular prism = 108cm2

The volume of the triangular prism = 48cm3

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Yes, y=x has an inverse.

Yes, y=x passes the horizontal line test.

If it didn't pass the horizontal line test, it would not have an inverse.

Question:

Write a linear function f with f (- 1/2) = 1 and f (0) = -4

The linear function f with f (- 1/2) = 1 and f (0) = -4 would be ; y = -5x -4.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

We are asked to write the linear function f with f (- 1/2) = 1 and f (0) = -4

Let the equation in variables x and y can be written in the form y = mx + c

So f (- 1/2) = 1

this gives, 1 = -1/2m+c      -----------eq 1

Also f (0) = -4

This gives -4 = c.            --------------eq2

Now Putting the value of c in the equation in eq1 we get m=0.

So 1 = -1/2m+c  

1 = -1/2m - 4

m = -5

Then we get;

y = -5x -4.

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Answer:

1/5

Step-by-step explanation:

these fractions are proper fractions

Answer: 1/

Step-by-step explanation:

Answer: 1. 3

5. -3

Step-by-step explanation:

Answer:

Each piece will be 4.9 inches long

Step-by-step explanation:

All you have to do is divide 14.7 by three as the rope itself is cut into 3 equal parts

therefore: 14.7/ 3= 4.9

Answer:

soda: 97

Hot dogs: 56

Step-by-step explanation:

S-sodas

H- hot dogs

S+H=153

41+H=S

Substitute equation

(41+H)+H=153

41+2H=153

-41.        -41

2H=112

/2.   /2
H=56

S+56=153

 -56.  -56

S=97

Hopes this helps please mark brainliest

Step-by-step explanation:

AC is the combination of AB and BC.

so, AB + BC = AC

(2n - 1) + (4n + 5) = 10n - 12

2n - 1 + 4n + 5 = 10n - 12

6n + 4 = 10n - 12

4 = 4n - 12

16 = 4n

n = 4

Answer:

A = 0.25*j + 1

Step-by-step explanation:

Answer:

[tex]A = 18 + \frac{j}{4}[/tex]

Step-by-step explanation:

A = 18 + j/4

A = Amount in $

Starting amount is 18 and a 1/4 dollar is earned for every cup of juice sold.

Answer:

x = 4

Step-by-step explanation:

Answer:

y = [tex]\frac{3}{4}[/tex] x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{3}{4}[/tex] , then

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation

to find c substitute (- 4, 5 ) into the partial equation

5 = - 3 + c ⇒ c = 5 + 3 = 8

y = [tex]\frac{3}{4}[/tex] x + 8 ← equation of line

Answer:

$90

Step-by-step explanation:

180x5 equal 00

$18x5 equals $90

Answer:

Step-by-step explanation:

There is only one line of symmetry:

because the one that is vertical is not representing symmetry.

Answer:

I hope this will help. Tip: reuse the formula!

Answer:

slope is the coefficient of x

so it is 6

good luck!!

the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243

the complete question is:

The demographic profile of Ecuador in 2018 is • 27.08% of the population are 0–14 years old • 18.35% are 15–24 years old • 39.59 are 25–54 years old • 7.53% are 55–64 years old • 7.45% are 65 years and older. In a random sample of 20 people, what is the probability that 2 are 65 years or older, 5 are 55–64 years old, 6 are 25–54 years old, 4 are 15–24 years old and 3 are 0–14 years old?

answer:

P(x) = P(x=2) + P(x=5) +p(x=6) +p(x=4) +p(x=3)

      =20[tex]C_{2}[/tex][tex](7.45)^{2}[/tex][tex](2.55)^{18}[/tex]+20[tex]C_{5}[/tex][tex](7.53)^{5}[/tex][tex](2.47)^{15}[/tex]+20[tex]C_{6}[/tex][tex](39.59)^{6}[/tex][tex](0.41)^{14}[/tex]+20[tex]C_{4}[/tex][tex](18.35)^{4}[/tex][tex](1.65)^{16}[/tex]+20[tex]C_{3}[/tex][tex](27.08)^{3}[/tex][tex](2.92)^{17}[/tex]

P(x) = 0.2424

the probability that 2 are 65 years or older, 5 are 55-64 years old, 6 are 25-54 years old, 4 are 15-24 years old and 3 are 0-14 years old IS 0.24243

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Answer: (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 )

Step-by-step explanation:

To write a polynomial in standard form, simplify and then arrange the terms in descending order. Expand (2x+1)(x−3) ( 2 x + 1 ) ( x - 3 ) using the FOIL Method.

Annie paid a total of $2.6 for 1.2 pounds of strawberries

In this question, we have the following parameters:

Unit cost per pound = $2.13 per pound

Number of pounds = 1.2 pounds

The amount paid for the number of pounds is represented by the equation

Amount paid = Unit cost per pound x Number of pounds

Substitute the known values in the above equation So, we have the following equation

Amount paid = 2.13 * 1.2

Evaluate the products

Amount paid = 2.556

Approximate

Amount paid = 2.6

Hence, the amount is $2.6

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Answer:

2.56

Step-by-step explanation:

The vertex of the function f(x) = x^2 + 12x is (-6, -36).

The concept that will be used here is the concept of Standard equation of a curve in vertex form.

The standard equation can be written as

f (x) = ax^2 + bx + c

Then the Vertex is the (h,k)

Then the X-coordinate of the vertex  can be written as (h = -b/2a) where  k = f(h)

If we compare the given equation with the standard form, then we have

a = 1, b = 12 and c = -10

Then we can input the values into the  (h = -b/2a)

h =[ -12/2(1)] = - 6

Then we can substitute the value of h in f (x) which is f(x) = x2 + 12x

k = f(h)= f (-6) =[ (-6)2 + 12 (-6)]

= [36 - 72] = -36

In conclusion the vertex is (-6, -36).

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The 20th term of the given arithmetic progression is 119.

An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).

3,6,9,12,15,18, and 21 are A.P. examples.

So, the formula for the nth term:

a+(n-1)d, where d is the common difference

Now, take out the equation:

6th term = 35

a+(6-1)d= 35

a+5d=35 ....(1)

13th term = 77

a+12d= 77 .....(2)

Then, subtract equation (1) from equation (2):

a+12d-(a+5d)= 77-35

a+12d-a-5d= 42

7d=42

d=6

Calculate from equation (1):

a= 35-5d= 35-5(6)= 35-30 = 5

20th term= a+19d= 5+19(6)= 119

Therefore, the 20th term of the given arithmetic progression is 119.

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Answer:

-11r

Step-by-step explanation:

4r - 9r = -5r

-5r - 11r = -16r

-16r + 7r = -11r

The value of f(-5) = -130

A cubic equation is an equation with degree three. All cubic equations have either one real root and two imaginary roots or three real roots. When polynomials have degree three, they are referred to as cubic polynomials.

A Cubic polynomial function is a polynomial function with the highest degree of exponents as 3. A cubic polynomial function has the following standard form:

Ax3 + bx2 + cx +d = 0

For the given question the cubic equation will be:

2x3 + bx2 + cx - 5 = 0

Given

Leading coefficient (a) = 2

Constant (T) = -5

f(1) = 0

f(2) = 9

Therefore the equation formed will be:

2x3 + bx2 + cx - 5 = 0

Now f(1) = 0

2(1)3 + b(1)2 + c(1) - 5 = 0

2 + b + c -5 = 0

b + c = 3  

b = 3-c -----(1)

On solving f(2) = 3

2(2)3 + b(2)2 + c(2) - 5 =3

16 + 4b + 2c – 5 =3

4b +2c = 3 – 11

4b + 2c = -8  ----(2)

Now substitute the b value in equation (2)

4(3-c) + 2c = -8  

12 – 4c +2c = -8

-2c = -20

C =10

Now substitute the c value in equation (1)

b= 3 – c

b = 3 -10

b = -7

Now substitute the b and c values in the cubic equation

2x3 - 7x2 + 10x - 5 = 0

Now calculate f(-5)

2(-5)3 - 7(-5)2 + 10(-5) - 5

= -250 + 175 – 50 -5

= -130

Therefore the value of f(-5) = -130

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The expression that represents the sum of the arithmetic series that has a first term of -12, a common difference of +7 and a number of terms of 5 is the option with the following;

An arithmetic series one that consists of the sum of an arithmetic sequence, such that each term of the series is obtained from the previous term by the addition or subtraction of a constant.

The series in the question is; -12 + (-5) + 2 + 9 + 16

The series in therefore a series of an arithmetic sequence

The equation of the series when the first term is -12 can therefore be presented as follows;

-12 + 7·k

Where;

-12 is the first term, 7 is the common difference, n is the number of terms, and k = n - 1

The above values for the terms of the series is obtained by using values of k that range from k = 0 to k = 4

The expression that represents the series is therefore the option;

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Answer: 11 cows and 19 chickens

Step-by-step explanation:

Applying the corresponding angles theorem, the measure of ∠HIJ = 33°.

If two triangles are similar to each other, their corresponding angles would be equal. Also, based on the corresponding angles theorem, corresponding angles are equal to each other.

Triangles IHJ and FGH are similar to each other, therefore, angles HFG and HIJ are corresponding angles.

Therefore:

The measure of angle HFG = the measure of angle HIJ

m∠HFG = 57 − 6x

m∠HIJ = −4x + 49

Thus:

57 − 6x = -4x + 49

Combine like terms

4x - 6x = -57 + 49

-2x = -8

Divide both sides by -2

-2x/-2 = -8/-2

x = 4

m∠HIJ = −4x + 49 = -4(4) + 49

m∠HIJ = 33°

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Complete Question:

In the diagram below of triangle FGH, I is the midpoint of FH and J is the midpoint of GH. If m∠HFG = 57 − 6x, and m∠HIJ = −4x + 49, what is the measure of ∠HIJ?

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

Given data;

Here, we present the dataset from the United Nations, which contains information on the number of kilowatt-hours of wind energy generated globally. The data set provides statistics on the US for 25 years, from 1990 to 2014, in millions of kilowatt-hours.

The linear equation for the first 11 years of data, from 1990 to 2000, must be determined.

To determine how much the actual value and anticipated value for the year 2001 differ in Quantity, we must first forecast the value for the year 2001 using our fitted equation with y-intercept.

It will be written as y = m(x) + c.

where,

The dependent variable is y. (in our example is quantity)

The independent variable is x. (in our example is the year)

'm' is equal to the slope of the variable X.

'C' is a constant.

The fitted equation is provided as follows:

Quantity = 186.87 (year) - 369274.72

Now that the value for the year 2001 has been provided,

Quantity = -1868.87 -369274.72 

Quantity = 4652.15

The value that the linear equation predicts for the year 2001 is 4652.15.

The precise figure for 2001 is 6806.

For the year 2001, the discrepancy between the actual and anticipated values is

6806 - 4652.15 = 2173.85

The distinction is 2173.85.

(2173.85/6806)*100 is the percentage difference.

As a result, the difference between the actual value and the forecasted value for the year 2001 is 31.94%.

Hence,

The value that the linear equation predicts for the year 2001 is 4652.15

The discrepancy between the actual and anticipated value is 2173.85

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Step-by-step explanation:

using Pythagoras theorem.

37,

x² = 6² + 8²

x = √6²+8² = 10ft

38.

13²=12²+x²

169 = 144 + x²

√169 - 144 = x = 5cm

hope it helps. :)

Answer:

x = 10 and x = 5

Step-by-step explanation:

using Pythagoras' identity

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

(36)

x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

x = [tex]\sqrt{100}[/tex] = 10

(38)

13² = x² + 12²

169 = x² + 144 ( subtract 144 from both sides )

25 = x² ( take square root of both sides )

[tex]\sqrt{25}[/tex] = 5 = x

x = 5

The amount of cookies baked was 28 cookies

let the number of pumpkin cookies be x

half of them on a plate for your brother and you

= x - x/2 = x/2

Your dog Gobbles ate six

= x/2 - 6

Your brother ate half of what was left

= (x/2 - 6)) / 2

= x/4 - 3

you ate the last four means that what was left is equal to 4

x/4 - 3 = 4

x - 12 = 16

x = 16 + 12

x = 28

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