The rectangular prism shown has a surface area of 488 square inches. What is the length of the prism?

Answer:

a) 165.52 degrees.

b)  131.41 degrees.

c)  118.96 degrees.

d)  159.73 degrees.

Step-by-step explanation:

The sine of an obtuse angle is positive as it is in the second quadrant.

a) Using a calculate the angle whose sine ( arcsin) is 0.25  = 14.478 degrees

so the obtuse angle  = 180 - 14.478 = 165.52 degrees to nearest hundredth

b) c) and d) are calculated in the same way.

Answer:

(5/2, -9/4)

Step-by-step explanation:

Answer: 4)

Step-by-step explanation:

Answer:

1st one is 3, 2nd is 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]6a^{2}=6534\\\\a^{2}=\frac{6534}{6}\\=1089\\\\a=\sqrt{1089}\\\\ a=33ft\\\\volume=a^{3}\\\\=33*33*33\\\\=35937[/tex]

To find the volume of a cube with a given surface area, we can use the formula for surface area and rearrange it to find the side length. Once we have the side length, we can calculate the volume of the cube.

To find the volume of a cube, we need to determine the length of one side. Since a cube has 6 equal sides, we can calculate the length of each side using the formula for surface area: surface area =  6 * side length * side length. Let's rearrange the formula to find the side length: side length = sqrt(surface area / 6). Once we have the side length, we can calculate the volume using the formula: volume = side length * side length * side length. Plugging in the given surface area of 6534 square feet, we find that the volume of the cube is approximately 2314 cubic feet.

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Answer:

$7

Step-by-step explanation:$1.50 + $2.50 will equal to $4. $4 added with$3 would be $7. There's your answer

Answer:

$36.94

Step-by-step explanation:

Okay, so. This is what we do. There is two magazines and they cost 9.95 each multiply 9.95 times 2

9.95 x 2 = 19.90

Okay, then he buys a book for 14.95 we add 19.9. and 14.95

19.90 + 14.95 = 34.85

Then we have a sales tax of 6% we would multiply 34.85 time 6%

34.85 x 6% = 2.09

Then we would add. 34.85 + 2.09

34.85 + 2.09 = 36.94

Therefore your answer is $36.94

Hope this helps!!!

The answer is $36.94. You add up the total purchases, multiply them by .06, then add that number to you total purchases.

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by  

3

gives the next term. In other words,  

a

n

=

a

1

⋅

r

n

−

1

.

Geometric Sequence:  

r

=

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of  

a

1

=

5

and  

r

=

3

.

a

n

=

(

5

)

⋅

(

3

)

n

−

1

Remove parentheses.

a

n

=

5

⋅

3

n

−

1

Answer:

2.4x+15.2

Step-by-step explanation:

Answer:

y=-12x

Step-by-step explanation:

equation to solve with: m=y2-y1/x2-x1

m=8-20/-3-2

Then solve for m which is the slope

m=-12/-1

m=-12

equation: y=-12x

Yo sup??

Equation of the given line is

y=12 - 0.5x

on the y axis the x coordinate will be , therefore at x=0 we get

y=12 - 0.5*0

y=12

Therefore the coordinates of the y intercept are (0,12).

Hope this helps.

Final answer:

The y-intercept for the equation y = 12 - 0.5x is found by setting x to 0, resulting in y = 12, giving us the coordinates of the y-intercept as (0, 12).

Explanation:

The equation of a straight line is given by y = mx + b, where m represents the slope of the line, and b is the y-intercept. In your case, the equation is y = 12 - 0.5x. To find the coordinates of the intercept on the y-axis, we set x to 0 and solve for y. This gives us the y-intercept directly from the equation without needing to graph it.

For the equation y = 12 - 0.5x, when x = 0:

y = 12 - 0.5(0)

y = 12 - 0

y = 12

Therefore, the coordinates of the intercept on the y-axis are (0, 12).

Answer:

  1/16

Step-by-step explanation:

Area is the product of linear dimensions.

Suppose the area of the triangle is the product of two dimensions p and q*:

  A = pq

Then the smaller triangle will have an area that is ...

  A = (1/4p)(1/4q) = (1/4)²pq = (1/16)pq . . . . . . 1/16 of the original area

__

If each of the linear dimensions of the triangle is multiplied by 1/4, the area will be multiplied by (1/4)² = 1/16.

_____

* No doubt, you have learned the area formula for a triangle is ...

  A = (1/2)bh

In the above, we might have p=1/2b and q=h. Or, there could be some other relationship between triangle dimensions and p and q.

The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Graph one line at a time in the same coordinate plane and shade the half-plane that satisfies the inequality.

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Answer: She purchased 8 sports drinks,

Step-by-step explanation:

Let be "d" the number of sports drinks that April purchased and "p" the number of slices of pizza that April purchased.

Set up a System of equations:

[tex]\left \{ {{d=p+3} \atop {2.25p+1.25d=21.25}} \right.[/tex]

In order to solve the System of equations you can use the Substitution Method:

1. Solve for "p" from the first equation:

[tex]d=p+3\\\\p=d-3[/tex]

2. Substitute it into the second equation:

[tex]2.25(d-3)+1.25d=21.25[/tex]

3. Finally, you must solve for "d" in order to find its value. You get that this is:

[tex]2.25(d-3)+1.25d=21.25\\\\2.25d-6.75+1.25d=21.25\\\\3.5d=21.25+6.75\\\\d=\frac{28}{3.5} \\\\d=8[/tex]

Answer:

Step-by-step explanation:

8 sport drinks

Answer:

x+y>1

Step-by-step explanation:

Answer:

One-sixth x + 47

1 and two-thirds x + 35 minus 1 and one-half x + 12

1 and one-third x + 35 minus 1 and one-half x minus 12

Step-by-step explanation:

The original expression in this problem is

[tex]5(\frac{1}{3}x+7)-3(\frac{1}{2}x-4)[/tex]

We start by applying the distributive property and multiplying each factor outside the brackets by each factor inside:

[tex]5\cdot \frac{1}{3}x+5\cdot 7 -3\cdot \frac{1}{2}x+3\cdot 4[/tex]

So we get:

[tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex]

Now we can rewrite this using mixed fractions:

[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+12[/tex] (1)

Which can be also written as

[tex]1\frac{2}{3}x+35-(1\frac{1}{2}x-12)[/tex] (2)

And finally, by solving it, we find

[tex]\frac{1}{6}x+47[/tex] (3)

So the three correct options are

One-sixth x + 47

1 and two-thirds x + 35 minus 1 and one-half x + 12

1 and one-third x + 35 minus 1 and one-half x minus 12

Answer:

[tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Slope = [tex]\frac{4-(-1)}{3-0} =\frac{5}{3}[/tex]

Answer:4 is thousands place

3 is hundredths place

8 is tens place

2 is ones place

Step-by-step explanation:

The place value of the underlined number 4,382 is,  

4 is thousands place

3 is hundredths place

8 is tens place

2 is ones place.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

The number 42,316 is different from 61,432 because the digits are in different positions.

here, we have,

the underlined number 4,382

so, we get the place value,

4 is thousands place

3 is hundredths place

8 is tens place

2 is ones place.

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The expression which gives the length of the transverse axis of the hyperbola is; Choice D; a-b.

The transverse axis is by definition, a line segment that passes through the center of the hyperbola and has vertices as its endpoints. The foci therefore lies on the line that contains the transverse axis. Hence, it follows that the correct answer choice is; a-b.

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To find the values of x and y requires solving equations, refining the solution through iterative methods like the extended Newton-Raphson technique, and validating results with approximation checks.

In answering this mathematical question, we are attempting to find specific values for the variables x and y. To solve for these variables, we employ various mathematical methods such as the Newton-Raphson technique for refinement.

Keeping the referenced data in consideration, the equations provided reveal that we manipulate these equations to gradually reach a more accurate result. For instance, taking the quadratic equation y²-0.30068y +0.022500 = 0 and using the quadratic formula y = 0.30068 ± √(0.30068)² – (4)(1)(0.022500) allows us to find the value for y, and an iterative process enhances the precision of x and y.

Remember to always retain a few extra significant figures to minimize rounding errors in the computational process. Additionally, entering our data into a calculator or a computer program will help in writing the linear equation, which needs to be rounded to an appropriate number of decimal places for accuracy. Examples mentioned illustrate evaluating the coordinates of a point, substituting values into equations, and analyzing the relation between variables through a graphical approach.

To validate our results, we compare the approximation to the actual value to ensure that our error margin is acceptable, especially when dealing with extrapolations from implicit differentiation in calculus contexts.

Final answer:

The volume of a pyramid with a height of 215 units and a square base of 339 units on each side is calculated using the formula V = (1/3)Bh, resulting in a volume of 1,304,688.67 cubic units.

Explanation:

To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. If the base is a square with each side being 339 units, then the area of the base (B) can be calculated as 339×339 square units. Given the height (h) of the pyramid is 215 units, the volume can then be calculated.

First, calculate the area of the base:
B = 339×339 = 114921 square units.

Then, use the volume formula by plugging in B and h:
V = (1/3)×114921×215 = 1,304,688.67 cubic units.

Therefore, the volume of the pyramid is 1,304,688.67 cubic units.

Answer:

The percentage of Guanine will be 17%

Step-by-step explanation:

As we know from Chargaff's rule, DNA from any organism will  contain 1:1 purine and pyrimidine ratio.

so, The adenine (Purine) ratio is 33% because the Thymine is 33%(Pyrimidine)

Then Guanine (Purine) will be 17% because the Cytosine (Pyrimidine) is  17%

Answer:

Therefore the area of the quadrilateral =35 cm²

Step-by-step explanation:

Given, the length of one of diagonal of quadrilateral is 10 cm and perpendicular drawn from the opposite vertices to this diagonal are the length of 2.8 cm and 4.2 cm.

A diagonal divided a quadrilateral into two triangle.

Therefore the area of the quadrilateral

= sum of the area of the triangles

[tex]=(\frac{1}{2}\times 10\times 2.8+ \frac{1}{2}\times 10\times 4.2)[/tex]cm²      [ area of a triangle[tex]= \frac{1}{2}\times base\times height[/tex]]

=35 cm²

Answer:

The deep of the sand will be 3.5 feet

Step-by-step explanation:

step 1

Find out the area of the court plus a 10-foot boundary around the  court for safety

[tex]A=(30+10+10)(60+10+10)\\A=(50)(80)\\A=4,000\ ft^2[/tex]

step 2

Find the deep of the sand

we know that

The volume of the sand is equal to

[tex]V=Ah[/tex]

where

A is the area of the base

h is the height or deep of the sand

substitute the given values

[tex]14,000=(4,000)h[/tex]

Solve for h

[tex]h=14,000/4,000=3.5\ ft[/tex]

Jerry's indoor beach volleyball court, including a 10-foot boundary, would have an area of 4,000 square feet, and with 14,000 cubic feet of sand, it would result in the sand being 3.5 feet deep.

Since Jerry wants to build an indoor beach volleyball court with a 10-foot boundary around it and has ordered 14,000 cubic feet of sand, we need to calculate the volume of the sand to determine how deep it will be when spread evenly over the entire area, including the boundary. The dimensions of the volleyball court are 30 feet by 60 feet, and adding a 10-foot boundary around it increases each dimension by 20 feet (10 feet on each side), resulting in a total area dimension of 50 feet by 80 feet.

To calculate the depth of the sand, we first calculate the area of the court including the boundary: Area = length × width = 50 feet × 80 feet = 4,000 square feet. Next, we divide the total amount of sand by the area to find the depth: Depth = volume / area = 14,000 cubic feet / 4,000 square feet = 3.5 feet deep. Therefore, if Jerry uses all the sand, it will be 3.5 feet deep.

Answer:

Area of the garden is [tex]306feet^2[/tex]

Step-by-step explanation:

Given:

Perimeter of the garden=84 feet

Let the width of the garden be 'W'

Length of the garden is 24 feet longer than the width of it

so, length of the garden= W+24 feet

To find the width 'W'

Perimeter of a rectangle= 2(Length+Width)

                                      [tex]84 =2(W+24+W)\\ 84 =4W+48\\ 84-48=4W\\ 4W=36\\ W=9[/tex] feet

Width=9 feet

Length=W+24= 9+24= 34 feet

Area of the garden= Length*width

                                 [tex]=34*9\\ =306 feet^2[/tex]

Area of the garden is 306 square feet

96 m

2 m/sec²

Step-by-step explanation:

Step 1:

In a velocity and time graph , the area which is under the plotted line represents the distance traveled

In the given graph , the plotted line from t=0 to t=4 ( for the first 4 secs) is a   triangle with base = 4 and height = 8

Area of this triangle is (1/2) * b * h = (1/2)* 4*8 = 16 m

Step 2 :

The plotted line from t = 4 to t = 14 is a rectangle with length equal to 10 and breadth equal to 8

Hence its area = length * breadth = 10 * 8 = 80 m

Step 3 :

Total  distance traveled is 80 + 16 = 96 m

Step 4 :

In the velocity time graph , slope denotes the acceleration at any given time. Since we want the acceleration for the first 4 secs, we need to find  slope of  line in from t = 0 to t= 4

when t = 0, v =0 and t= 4, v = 8

Slope = 8-0/4-0 =2 m/sec²

Answer:

[tex]Give\ Two\ expressions\ are\ equivalent.[/tex]

Step-by-step explanation:

[tex]First\ expression=7^2+4x\\\\At\ x=2,\ value\ of\ first\ expression=7^2+4\times 2=49+8=57\\\\Second\ expression=4x+(7\times 7)\\\\Second\ expression=4x+7^2\ \ \ \ \ \ \ \ \ \ \ as\ m\times m=m^2\\\\Second\ expression=7^2+4x\ \ \ \ \ \ \ \ using\ commutative\ property\ of\ addition\\\\At\ x=2,\ value\ of\ second\ expression=7^2+4\times 2=49+8=57\\\\Hence\ these\ two\ expressions\ are\ equivalent.[/tex]

Answer:

This is Equivalence system of equations. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2

The answer is 12 :)

The number of rows she had been completed before Elena started working is 12 rows.

Suppose the considered function whose graph is to be made is

f=f(x) f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f=f(x) f(x)

are plotted on the vertical axis.

They are together plotted on the point

f(x)) (x,y) = (x, f(x))

This is why we usually write the functions as:

f(x) y = f(x)

We are given that;

The points= (14,19), (20,22), (30,27)

Now,

To find the number of rows completed before Elena started working, we need to find the equation of the line that passes through the given points on the graph.

Using the slope formula, we can find that the slope of the line is (27-22)/(30-20) = 0.5.

Using the point-slope form of a line, we can write the equation as y - 22 = 0.5(x - 20).

Simplifying the equation, we get y = 0.5x + 12.

To find the y-intercept, which is the number of rows completed before Elena started working, we plug in x = 0 and get y = 12.

Therefore, by the given graph the answer will be 12 rows.

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The complete question is;

Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting. The points on graph are (14,19), (20,22), (30,27).

Assuming she worked at a constant rate, how many rows had been completed before Elena started working?

Answer: use calculated

Step-by-step explanation:

Calculator

Answer:

Everything

Step-by-step explanation:

-6(n-8)=4(12-5n)+14n    Given

-6n+48=48-20n+14n    Distribute

-6n+48=48-6n          Simplify

-6n=-6n                Subtraction Property of Equality(Subtract 48 from both sides)

n=n                   Division Property of Equality(Divide both sides by -6)