how do i do these types of problems?

The amount of wrapping paper used by Gavin to wrap a triangular prism box is 647.75 m².

What is a prism?

A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.

The formula for area of rectangle is -

Area = length × breadth

The area of rectangle ABFG is -

Area = AB × BF

The value for line segment AB = 15 m

The value for line segment BF is -

BF = BC + CE + EF

BF = 14 + 7 + 15.65

BF = 36.65 m

So, the area of rectangle ABFG is -

Area = 15 × 36.65

Area = 549.75 m²

Now, the triangular prism has triangle part left.

The formula for area of triangle is -

Area = 1/2 × base × height

So, the area of triangle IJH is -

Area = 1/2 × IJ × JH

The value for line segment IJ = 14 m

The value for line segment JH = 7 m

So, the area of triangle IJH is -

Area = 1/2 × 14 × 7

Area = 49 m²

Since, there are two triangles (Δ IJH = Δ CDE ) so the area of total shape is -

Total area = Area of ABFG + 2(Area of Δ IJH)

Total area = 549.75 + 2(49)

Total area = 647.75 m²

Therefore, the area of triangular prism box is 647.75 m².

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Answer:

  G  descends about 8 ft per second

Step-by-step explanation:

You want to know the descent rate of an airplane whose altitude is shown on a graph as being 1500 ft at 0 seconds and 0 ft at 180 seconds.

The airplane descended 1500 feet over a period of 180 seconds. That rate of change is ...

  (-1500 ft)/(180 s) ≈ -8.333 ft/s

The plane descends about 8 feet per second.

__

Additional comment

The slope of the line segment is the change in y divided by the change in x. For computing these changes, it is useful to consider points whose coordinates are obvious. Here, the y-intercept (1500 ft) and the x-intercept (180 seconds) are good choices.

The change in y from 1500 to 0 is a change of -1500. The change in x from 0 to 180 is a change of +180. The ratio of these changes is the slope, which is often designated by the letter m:

  m = -1500/+180 = -25/3 = -8 1/3 . . . . . . about -8

The units of the slope are the ratio of the y-axis units to the x-axis units: feet/second.

The slope of -8 feet/second tells you the plane is descending about 8 feet per second.

Let's call the length of the longer rope piece x and the length of the shorter rope piece y. We know that:

x + y = 5 (the total length of the rope is 5 feet)

And from the problem statement, we have:

3x - 7 = 5y

Now we can use the first equation to solve for y:

y = 5 - x

Substituting this expression for y into the second equation:

3x - 7 = 5(5 - x)

Expanding the right side:

3x - 7 = 25 - 5x

Adding 5x to both sides:

8x - 7 = 25

Adding 7 to both sides:

8x = 32

Dividing both sides by 8:

x = 4

So the length of the longer rope piece is 4 feet.

Answer:

y = 2ˣ

Step-by-step explanation:

Since, the question asked which function is best represented by the graph and the function given are:

y = 0.5ˣ

y = 2ˣ

y = 3ˣ

y = 2 * 0.25 ˣ

We can graph each of them to see which is the answer.

Base on the graph below we can see that;

the function that represents the graph is  y = 2ˣ

RevyBreeze

Answer:

DE = 6 cm

Step-by-step explanation:

The concept behind this question is the Chord-Chord Power Theorem. This product states that "if two chords intersect in a circle, then the products of the lengths of the chords segments are equal". In this case:

CE × DE = AE × BE

4 × DE = 8 × 3

4 × DE = 24
DE = 6 cm

Hope this helps!

Since in the figure, a || b and m∠1 = 34°, the magnitude of m∠5 is equal to 34°.

In Mathematics, parallel lines are two lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to lines a and b, we have the following:

m∠1 ≅ m∠5

m∠5 = 34°.

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The restocking fee for an item with an original price of $180 and a restocking fee of 6% is $10.80.

A restocking fee is a fee that is charged when a customer returns an item, usually to cover the costs associated with processing the return and getting the item back in a sellable condition. The fee is typically calculated as a percentage of the original price of the item.

In this problem, we are given that the restocking fee is 6% and the original price of the item is $180. To find the restocking fee, we can use the formula:

Restocking fee = (Percentage fee / 100) x Original price

In this case, the percentage fee is 6% or 0.06 (since 6% is equivalent to 6/100). The original price is $180. Substituting these values into the formula gives:

Restocking fee = (0.06) x $180

Restocking fee = $10.80

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4. The value of b is 180+2a (option C)

11. the distance between A and B is 4√2 (option A)

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.

The total angle at a point is 360°

therefore the third angle in the triangle = 180-(a+a) = 180-2a

therefore b = 360-( 180-2a)

b = 360-180+2a

b = 180+2a

If the volume of the cube is 64, then AB = √4²+4²

= √16+16 = √32

AB = √32

AB = √ 16×2

AB = 4√2

Therefore the distance between A and B is 4√2

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The right response is, "5 hexagons are made up of 15 pattern block trapezoids."

Geometric shapes known as pattern block trapezoids are frequently utilized in arithmetic instruction. On a flat surface, they are one of a number of forms that can be used to make tessellations, or repeating patterns. Different colored plastic or foam pattern block trapezoids are available in a variety of sizes, with each color denoting a distinct size and form. Pattern block trapezoids are frequently used to teach geometry principles like area, perimeter, and angles in addition to their application in making tessellations. They can also aid in the development of kids' spatial reasoning and problem-solving skills.  

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"3 added to 5 is the same as 3 more than 5",  this statement is true. The statement "3 added to 5 is the same as 3 more than 5" means that the expression "3 added to 5" is equal to the expression "3 more than 5".

Another way to express the equality of two mathematical expressions is "3 added to 5 is the same as 3 more than 5".

"3 added to 5" is equivalent to the sum "3 + 5", which equals 8.

"3 more than 5" can be written as "5 + 3," which equals 8 as well.

Because both expressions have the same value of 8, the statement "3 plus 5 equals 3 more than 5" is correct.

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The complete tables for the given equations is:-

For y = 3x

X   Y

1     3

2    6

3    9

For y = -2x + 5

X   Y

1    3

2   1

3   -1

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The given two equations are;-

y = 3x

y = -2x +5

The different points passing through the line y =3x are:-

X   Y

1     3

2    6

3    9

The different points passing through the line y =-2x + 5 are:-

X   Y

1    3

2   1

3   -1

The graph of the points and the line as is attached with the answer below.

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Answer: look at the image for the answer and the solution

Step-by-step explanation:

Answer: a^2 b^2 c^2

Step-by-step explanation:

because that is the pythageoran theorem the rule of it is a^2 + b^2 + c^2 so it's right

Un-simplified rate of dollars-gallons = 22.5/9  $ and and gallons to dollars 9/22.5 $ .  and simplified rate of dollars-gallons = 22.5/9  $ = 2.5 and and gallons to dollars 9/22.5  = 0.4 .

Here first we have to calculate the rate of gallons of gas as per gallons so for that we will find the rate of 1 gallons for that we will divide the  22.4$ to 9 gallons so ans is 22.5$/9 is the rate for 1 gallons

and 2nd we have to calculate the amount of gas as per $ like we have to calculate the the amount if we spend 1 $  so for that we will divide 9 gallons / 22.5$ = 9/22.5

And here in 1st part we  are not calculate the ans in decimal as we have to calculate this on un-simplified  ans .

and in 2nd part we calculate it .

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The width of standard television set is 16.8 inches.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

We can solve this by using the  Pythagorean theorem which is below:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Or we can say

[tex]w^{2} +h^{2} =d^{2}[/tex]

w = width

h = height

d = diagonal measure

With that said, we know the height is .75 times the width so .75w. We also know d = 21, which is our diagonal measure.

w = don't know yet but need to find

h = .75w

d = 21

[tex]w^{2} +h^{2} =d^{2}[/tex]

[tex]w^{2} +(0.75w)^{2} =21^{2}[/tex]

1.5625 w^2 = 441

w^2 = 441/1.5625

w ^2 = 282.24

w =16.8

The width of standard television set is 16.8 inches.

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The total cost of an order is $900 if 50 invitations cost is $298.50

To calculate the cost of an order of personalized invitations, you would need to know the cost of each invitation and the one-time design fee.

Let calculate the cost of each invitation and the one-time design fee as follows:

50 Invitations: $298.50 / 50 = $5.97 per invitation

500 Invitations: $2049 / 500 = $4.098 per invitation

Design Fee: ($2049 - ($5.97 × 50)) / 500

= $3.90 one-time design fee

If you wanted to order 150 personalized invitations, the cost would be:

150 Invitations x $5.97 per invitation = $896.50

Plus one-time design fee of $3.90 = $890.40

Total cost = $896.50 + $3.90 = $900.

Hence, the total cost of an order is $900 if 50 invitations cost $298.50

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The first term of an arithmetic progression is 5 and the 10th term is 95. The sum of the first 10 terms is 455.

The sum of the first 10 terms of an arithmetic progression (A.P.) can be found using the formula:

S_n = n/2 * (2a + (n-1)d)

where a is the first term, d is the common difference, and n is the number of terms.

Given that the first term is 5 and the 10th term is 95, we can find the common difference (d) using the formula:

a_n = a + (n-1)d

Plugging in n = 10 and a = 5, we get:

95 = 5 + (10 - 1)d

Solving for d, we get:

d = (95 - 5) / (10 - 1) = 9

Now that we know the common difference, we can find the sum of the first 10 terms:

S_10 = 10/2 * (2 * 5 + (10 - 1) * 9) = 10/2 * (10 + 81) = 10/2 * 91 = 455

So, the sum of the first 10 terms is 455.

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In a case whereby Shana bought sodas and popcorn for the movies. Sodas cost $3 each and popcorn costs the system of equation involving the number of sodas, s, and the bags are:  (3s + 4p )= $26  and s+p = 7 .Then Shana bought 5 sodas and 2popcorn.

We know that :

Sodas cost =$3 each

popcorn costs= $4 per

total =$26

The system of equation can be written as :

(3s + 4p )= $26

We were also told that he bought things equal to the 7 things which can be expressed as:

s+p = 7

Then we can solve the equations as:

3s + 4p = 26 .............................................(1)

s+p = 7................................................................(2)

multiply equation by -3

-3s - 3p =-21  ..................................................................(3)

Then add (1) and 3

4p-3p = 26-21

p=5

Then substitute the value of p into equation 2 we have

s+5 = 7

s= 7-5

=2

s=2

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complete question:

Shana bought sodas and popcorn for the movies .Sodas cost $3 each and popcorn cost $4 per bag . Shana bought 7 things from the concession., all either sodas or bags of popcorn. Shana spent a total of $26 . Write a system of equations involving the number of sodas S ,and the bags of popcorn ,B .Solve the system to see how many of each shana bought

The expression for the given model will be 3÷2/5.

What exactly are expressions?

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.

Now,

as shown in figure the model is shaded uptil 3

and in 1 unit there are 5 total boxes which are divided in 2 parts

Therefore, it will be represented by 3÷2/5.

Hence,

         The expression for the given model will be 3÷2/5.

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Solution of given inequality is x < -12.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

Given inequality

- (1/2)x > 6
Multiplying with 2 on both sides

- (2/2)x > 6×2

- x > 12

Multiplying with -1 on both sides

x < -12

Hence, x < -12 is the solution of given inequality.

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Answer: 1.08g

Step-by-step explanation:

Concentration = Moles/ Volume

Moles = Concentration x Volume

Moles = 0.048 x 250/1000

Moles= 0.012

Moles= Mass / Relative Formula Mass

Mass = Moles x Relative Formula Mass

Mass = 0.012 x 90

= 1.08g

The value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2

We shall evaluate for the value of x to know what makes the algebraic equation true as follows;

3(2x - 5 + 8x) = 5(2x + 5)

3(10x - 5) = 5(2x + 5)

30x - 15 = 10x + 25 {expand bracket}

30x - 10x = 25 + 15 {collect like terms}

20x = 40

x = 40/20 {divide through by 20}

x = 2

Therefore, the value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2.

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The greatest common factor of the 24x³ + 36x² is 12x².

It is the greatest factor common to all the numbers given such that there are no greater factors common other than that.

Example:

4 is the gcd of 12, 8, 16.

We have,

24x³ + 36x²

Taking out the common factor.

= 12x² (2x + 3)

Thus,

GCF of the expression is 12x².

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The percentage of decrease in the amount of land that Simon owns is 20.1%.

1,510 - 1,208 = 302

302 / 1,510 = 0.201

0.201 x 100 = 20.1%

Simon recently sold his old farmland, which was 1,510 acres in size, and purchased a new plot of land that is 1,208 acres in size. To calculate the percent of decrease in the amount of land that Simon owns, we subtract the new land size from the old land size and divide the result by the old land size. This number is then multiplied by 100 to get the percent of decrease. In this case, we subtract 1,208 from 1,510 to get 302. We then divide 302 by 1,510 to get 0.201. When we multiply 0.201 by 100, we get 20.1%, which is the percent of decrease in the amount of land that Simon owns now.

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The angle to the nearest tenth of a degree, we round the result to 50.7 degrees.

In trigonometry, cosine is a function that takes an angle as an input and produces a numeric value between -1 and 1 as an output. The cosine of an angle A is represented by cos A. In this problem, cos A is given to be 0.8945. To find the angle, we can use the inverse cosine function (or arccosine) which returns the angle in radians. To obtain the angle in degrees, we can multiply by 180/π (which is equal to 57.2958). The angle A is then equal to 50.6 degrees.  To find the angle to the nearest tenth of a degree, we round the result to 50.7 degrees.

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Answer:

The total length of the two straight parts is 80 m x 2 = 160 m.

So, the length of the curved part of the track is 400 m - 160 m = 240 m.

Let the radius of the curved part of the track be "r".

Since there are two curves, each of length "l", in the track, the total length of both curves is 2l.

The length of one curved part can be given by the formula:

l = 2πr, where π is pi (approximately equal to 3.14).

So, 2l = 2 x 2πr = 4πr.

Therefore, 4πr = 240 m.

Dividing both sides by 4π, we get:

r = 240 m / (4π) = 240 / (4 x 3.14) = 15 m.

Hence, the radius of the curved part of the track on both sides is 15 m.

The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)

A graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:

y = ax^2 + bx + c,

where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.

A graph of a linear equation is a straight line. A general form of a linear equation is given by:

y = mx + b,

where m is the slope of the line and b is the y-intercept.

In this problem, the ordered-pairs will be the point in which they intersect with each other.

Looking carefully at the graph, the ordered pair will be at points

A = (-2, 7)

B = (2, -1)

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