Recall that two angles are complementary if the sum of their measures is 90°. Find the measures of two complementary angles if one angle is 15º more than two times the other angle. ​What does the smaller angle measure? What does the bigger one measure?

A pyramid is a solid shape with a specified shaped base. The required answer is 8.67 cubic feet.

A pyramid is a solid shape with a specified shaped base. While a square based pyramid is a type of pyramid which has its base to be a square.

Volume of a square based pyramid = [tex]\frac{1}{3}[/tex] x base area x height

Also, are of a square = length x length

So that,

i. For the first pyramid;

volume =  [tex]\frac{1}{3}[/tex] x (2 x 2) x 6

            = 8 cubic feet

The volume of the first pyramid is 8 cubic feet.

ii. For the second pyramid, we have;

height = 8 feet

base side = 2.5 feet

So that.

Volume =  [tex]\frac{1}{3}[/tex] x (2.5 x 2.5) x 8

             = 16.6667

Volume = 16.67 cubic meters

The volume of the second pyramid is 16.67 cubic meters.

Therefore, the volume of the second pyramid is greater than the volume of the first pyramid by;

volume of the second pyramid - volume of the first pyramid = 16.67 - 8.0

                                              = 8.67 cubic feet

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The function f(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.

Graph is a mathematical representation of a Networks and it's describes the relation between lines and points.

The graph of the function f(x) is given.

The following steps can be used in order to determine the interval for f(x):

Step 1 - The value of f(x) means the value of y.

Step 2 - The value of f(x) is positive when the graph of f(x) is in the first or in the second quadrant.

Step 3 - So, according to the graph function f(x) is positive when the value of x is in between -3 and 5.

Therefore, the correct option is 3).

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Answer:

x=2√10,−2√10

Step-by-step explanation:

The equation of line where the y intercept is -3 and slope is 4/5 is

y = ( 4/5 )x - 3

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the equation A is y = mx + b

The y intercept of the line b = -3

The value of b = -3

The slope of the line m = 4/5

The value of m = 4/5

Now , substituting the values in the equation of line , we get

y = mx + b

y = ( 4/5 )x + ( -3 )

y = ( 4/5 )x - 3

The graph of the equation y = ( 4/5 )x - 3 is given below

Therefore, the value of the equation of line A is y = ( 4/5 )x - 3

Hence , The equation of line where the y intercept is -3 and slope is 4/5 is

y = ( 4/5 )x - 3

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The area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

Given that, the dimensions of a rectangle (x-1) and (x+3).

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Here, the area of a rectangle

= (x+3)×(x-1)

= x²+3x-x-3

= x²+2x-3

Hence, the area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the area of a rectangle with the dimensions (x-1) and (x+3).

Answer: To find out how long it takes the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the paddle wheel and divide that by the speed at which the fins along the outer edge are traveling.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius of the circle.

The radius of the paddle wheel is 2 feet (the diameter of 4 feet divided by 2), so the circumference is:

C = 2π * 2 = 8π feet

To find out how long it takes the paddle wheel to complete 100 full revolutions, we divide the number of feet traveled in one revolution (the circumference of 8π feet) by the speed at which the fins are traveling (1.3 feet per second):

100 * 8π feet / 1.3 feet per second = 615.38 seconds

Rounded to the nearest second, it takes approximately 615 seconds for the paddle wheel to complete 100 full revolutions.

Answer: $50.25

Step-by-step explanation:

     First, we will write an equation to represent this situation.

C = $2.75 + $5D

     Next, we will substitute 9.5 miles into D and solve.

C = $2.75 + $5D

C = $2.75 + $5(9.5)

C = $50.25

Answer:

(a) c = 2.75 + 5d

(b) $50.25

Step-by-step explanation:

(a)

The information tells us the following:

Cost of a taxi ride = $2.75 + (5 * number of miles travelled)

We can use the variables c and d to represent the descriptions:

c = 2.75 + 5d

(b)

Substitute 9.5 into the equation as d:

c = 2.75 + 5(9.5)

Simplify:

c = 2.75 + 47.5

c = 50.25

Therefore, the cost of a 9.5 mile ride is $50.25.

Answer:

20 boxes

Step-by-step explanation:

12 cans = 1 box

240 = x

apply rule of three

(240/12) x 1 = x

20 = x

Answer:

She will need 20 boxes

Step-by-step explanation:

Take the total number of cans and divide by the number of cans per box

240/12

20

She will need 20 boxes.

Answer:

False

Step-by-step explanation:

Subtract the numbers  115 − 10 = 105    

     2.Simplify 12 − 5(2 − 6) : 8

105=8

this shows that the sides are not equal so it is false  

The length of the two arcs and the area of the two circular sectors can be calculated as follows:

Since the semicircle is divided into two circular sectors, each sector has an angle of 180/2 = 90 degrees. Therefore, the smaller circular sector has an angle of 90 * (4/5) = 72 degrees, and the larger circular sector has an angle of 90 - 72 = 18 degrees.

The length of the arc of a circle is equal to the circumference of the circle multiplied by the ratio of the central angle of the arc to 360 degrees. Therefore, the length of the smaller arc is 18 * pi * (72/360) = 8pi cm, and the length of the larger arc is 18 * pi * (18/360) = 2pi cm.

The area of a circular sector is equal to the area of the circle multiplied by the ratio of the central angle of the sector to 360 degrees. Therefore, the area of the smaller circular sector is 18^2 * pi * (72/360) = 288pi cm^2, and the area of the larger circular sector is 18^2 * pi * (18/360) = 72pi cm^2.

Therefore, the length of the two arcs is 8pi cm and 2pi cm, and the area of the two circular sectors is 288pi cm^2 and 72pi cm^2.

The distance between the point and the line is 3 units.

Find the equation for line L

Begin by finding the slope of the line through the given points, (4,-1) and (4,9) ; its intercept:

m = (y₂ - y₁) / (x₂ - x₁)

= (9 - (-1) ) / 4 - 4

= 10 / 0

= Undefined

Because the slope is undefined, then line L is a vertical line which has an x-intercept of (4,0):

x=4

Because, line L is vertical, then the line w perpendicular to it is a horizontal line that passes through (1,6)(1,6) so its equation is y=6. Hence, L and w intersect at (4,6) which we will denote as Q.

The perpendicular distance is the distance from point P(1,6) to point Q(4,6) which is simply the absolute value of the difference of the x-coordinates:

d = | 1 - 4 |

= |-3|

= 3

Hence, The distance between the point and the line is 3 units.

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Answer:

I think it's 3650000

Step-by-step explanation:

7.1 mil ÷ 2 = 3550000

3550000 + 100000 = 3650000

Answer:

y = - [tex]\frac{5}{4}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-5}{4-0}[/tex] = [tex]\frac{-5}{4}[/tex] = - [tex]\frac{5}{4}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ b = 5

y = - [tex]\frac{5}{4}[/tex] x + 5 ← equation of line

Under the same translation as X and X' the coordinates of Y' = (-2, -4) and Z' = (-4, -1)

What is translation of a point in coordinate system?

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

According to the given question:

It is given about the points X (-4, -2) and X' (-6, -5).

We see that the translation is moving -2 units horizontally to the left and -3 units vertically down.

Therefore, the point Y(0,0)  is translated to Y'(0-2,-1-3) = Y'(-2,-4)

and the point Z(-2,2)   is translated to Z'(-2-2,2-3)  = Y'(-4,-1).

Hence, under the same translation Y' = (-2, -4) and Z' = (-4, -1)

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The number of swims that Will swims by using decimal divisions is 16 laps in each hour.

What is decimal division?

When dividing decimals, the divisor must be converted to a whole number by moving the decimal point to the right. The dividend's decimal point is then carried up to the same number of places to the right, and the resulting numbers are divided in the same manner as regular long division.

Given, Will swims a total of 45.6 laps in 2.85 hours

That is, 2.85 hours = 45.6 laps

or, 1 hour = 45.6/2.85 = 16 laps

Hence, he swims 16 laps each hour.

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The smallest integer out of the three integers is 109

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Three consecutive integers:

x, x+1, x+2

The sum of the integers,

x+(x+1)+(x+2) = 330

3x + 3 = 330

3x= 327

x= 327/3

x= 109

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Step-by-step explanation:

The given mass of the Earth is 5.972 × 10²⁴

The given mass of the Jupiter is 1.898 × 10²⁷

Now,

1.898 × 10²⁷ ÷ 5.972 × 10²⁴

= 0.3178 × 10³ = 317.8

Thus, Jupiter is 317.8 heavier than Earth

180 - 57 = 123 ( ALLIED ANGLE )

The journal entry for the July 31 sales and November 11 cash payment is shown below .

In the question ,

it is given that ,

the amount for which Qantas Industries sold electronics during July under a nine-month warranty is = $325000  ,

cost to repair defects is = 4.5 percent of sales price .

So , the cost to repair is = 4.5% × 325000 = $14625 .

So , the journal entry for July 31 is

Warranty expense    Debit   14625

Estimated warranty liability/warranty payable    Credit   14625

and the journal entry for November 11 is :

Estimated warranty liability /warranty payable    Debit    220 ,

                                                                Cash       Credit   220  .

Therefore , the Journal entry is shown above .

The given question is incomplete , the complete question is

Qantas Industries sold $325,000 of consumer electronics during July under a nine-month warranty. The cost to repair defects under the warranty is estimated at 4.5% of the sales price. On November 11, a customer was given $220 cash under terms of the warranty. Provide the journal entry for the estimated warranty expense on July 31 for July sales. Provide the journal entry for the November 11 cash payment .

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The line AC from the diagrammatic expression of the tangent of the circle shows that line AC is 24.0

A tangent of a circle is a line that intersects the circle at a single point. The site at which the tangent intersects the circle is referred to as the site of tangency.

From the given information:

Line |CD| =  Diameter

Line |EA| = radius = 18

Line |DB| = 12

Then, we can infer that line EA = DE since they are both (radii of the circle.)

Line |DE| = |EA| = 18

By using the formula for Pythagoras' theorem, we can find line |EA|.

hyp² = opp² + adj²

where;

Line |BE| = hypotenuse = DB + BE = 12 + 18 = 30

Line |AB| = opposite (x) = ???

Line |EA| = adjacent = 18

Thus;

30² = x² + 18²

900 = x² + 324

-x²  = -900 + 324

x  = √576

x = 24.0

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Answer:

[tex]\frac{7}{5}[/tex] or 7:5

Step-by-step explanation:

You are going from the smaller triangle to the larger.

Let x = the scale factor.  Find two corresponding sides that you know both lengths.

50x = 70  Divide both sides by 50

x = [tex]\frac{70}{50}[/tex]  Divide both the numerator and denominator by 10

[tex]\frac{7}{5}[/tex]

Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is [tex]0.78[/tex].

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

For a family living in Southern Mississippi, the probability of owning a dog is [tex]0.4[/tex], the probability of owning a cat is [tex]0.5[/tex], and the probability of owning both a cat and a dog is [tex]0.12[/tex].

Probability od owing a dog is

[tex]P(A)=0.4[/tex]

Probability of owing a cat is

[tex]P(B)=0.5[/tex]

Probability pf owing both a cat and a dog is

[tex]P(A[/tex]∩[tex]B)=0.12[/tex]

As we know,

[tex]P(A[/tex]∪[tex]B)=P(A)+P(B)-P(A[/tex]∩[tex]B)[/tex]

[tex]P(A[/tex]∪[tex]B)=0.4+0.5-0.12[/tex]

[tex]P(A[/tex]∪[tex]B)=0.78[/tex]

Hence, the probability that a family living in Southern Mississippi owns a cat or a dog is [tex]0.78[/tex].

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Amount of computer can be 350 or more than 350.

What do you mean by inequality?

Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.

Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.

It is given that Alex has $600 in her checking account and She wants to have at least $250 left in her checking account after buying the computer.

Let the amount of computer be t

According to the question , inequality become:

600 - t ≥ 250

600 - 250 ≥ t

350 ≥ t

Therefore, amount of computer can be 350 or more than 350.

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Answer: y= -3x -1

Step-by-step explanation: y=mx+b

The Y-intercept is at (0,-1), so b is -1

The slope is rise/run, and the graph is down 3, right 1, so the slope is -3/1

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If a prestigious program accepts 2 out of every 9 applicants per year than the program will accept 360 applicants out of 1620.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

the ratio is given:

2/9 = 360/x

solving for the value of x;

x/9=360/2

x=(180)9

x=1620

this is the required value of applicants that were not accepted.

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Answer:

18 miles.

Step-by-step explanation:

You start with 12 miles and then you first need to figure out what 5% of that is by doing the equation x/12 = 5/100 and you will then get .6. Then you multiply that number by 10 (one for each week) getting 6. Then you add the 6 to your starting total to get 18.

Answer: 39.23 miles per hour

Step-by-step explanation:

1 day = 24 hour

3 days = 72 hours

Add one more hour for both to get to 9 AM, so it will take 73 hours to get there.

Now we find the average rate of change.

We take 2864 divided by 73 = 39.23 miles per hour