an equilateral triangle has side lengths of 28 m what is the length of its altitude

Perry's paycheck was $100. To find Perry's paycheck, we can work backward from the final amount he had after finding $10 and ending up with $24.

Let's denote Perry's paycheck as "x". After buying the shirt and jeans, he spent a total of $26 + $52 = $78. So he had "x" - $78 left. He then spent half of what he had left on a snack, leaving him with 1/2 * ("x" - $78) = 1/2*x - $39.

When he found $10, he ended up with $24, so we can set up the equation:

1/2*x - $39 + $10 = $24

Simplifying this equation gives us:

1/2*x = $53

Multiplying both sides by 2, we get:

x = $106

Therefore, Perry's paycheck was $100.

In summary, we used a series of calculations to work backward from the final amount Perry had to determine his original paycheck. We accounted for the amount he spent on a shirt, jeans, and a snack, as well as the amount he found on his way home.

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By answering the presented question, we may conclude that Therefore, the perimeter of the classroom is 96√2 + 42 feet (approx. 155.27 feet).

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a hexagon that is fundamental rule, or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

The perimeter-

d = √[(x2 - x1)² + (y2 - y1)²]

So, the perimeter of the classroom is:

d1 = √[(-12 - (-12))² + (15 - (-9))²] = √(24² + 24²) = √(2² × 24²) = 48√2

d2 = √[(-12 - 9)² + (15 - 15)²] = √(21²) = 21

d3 = √[(9 - 9)² + (15 - (-9))²] = √(24² + 24²) = √(2² × 24²) = 48√2

d4 = √[(9 - (-12))² + (-9 - 15)²] = √(21²) = 21

perimeter = d1 + d2 + d3 + d4

= 48√2 + 21 + 48√2 + 21

= 96√2 + 42

Therefore, the perimeter of the classroom is 96√2 + 42 feet (approx. 155.27 feet).

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He bought 4.29 Kilos of fruit.

4+0.29=4.29

Luke bought 4.29 kilograms of fruit in all

Step-by-step explanation:

Simple addition will be used to find the total fruit Luke bought.

Given

Amount of apples he bought  = 4 kilograms

Amount of oranges he bought = 0.29 kilograms

so the total fruit will be:

[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]

[tex]=4+0.29[/tex]

[tex]=4.29[/tex]

So,

Luke bought 4.29 kilograms of fruit in all

Keywords: Measurement, addition

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Answer:

the test does not provide convincing evidence that the proportion is greater than 90%

Answer:

Choice 2
∠1 and ∠7, ∠2 and ∠8

Step-by-step explanation:

This is a good example of a problem that can be solved by POE(process of elimination)

First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°

The same applies for ∠3 and ∠4 (third choice)

The same applies for ∠1 and ∠4 (fourth choice)

That leaves choice 2

We can prove ∠1 ≅ ∠7 as follows:

∠1 ≅ ∠3 since they are vertically opposite angles

∠3 ≅ ∠7 since they are exterior angles

So ∠1 ≅ ∠7

By similar reasoning,
∠2 ≅ ∠8

So correct choice is Choice 2

The slope between the points (-3, 0) and (0, -1) is -1/3.

The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.

Let us consider the first two points (-3, 0) and (0, -1).

The slope of the line is given as:

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

Substituting the values we have:

m = (-1 - 0) / (0 - (-3)) = -1/3

Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.

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Answer: 1500000

Step-by-step explanation:

use a calculator

Answer:

1,500,000

Step-by-step explanation:

Breaking it up into an easier problem:

20x50 = 1,000

30x50=1,500

1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.

Thus, the answer is 1,500,000

To estimate the distance traveled  we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.

A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.

The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.

Using the trapezium rule, the estimated area of each strip is:

Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s

Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s

Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s

Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s

The total estimated area is the sum of the areas of the 4 strips:

Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s

Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:

Estimated distance traveled is = |-4000| = 4000 meters

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Using trigonometric functions, the value of the side AC = 2.85 units.

The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.

The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of  f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.

Now in the given figure,

The angle is a right-angled triangle.

Now as per the trigonometric functions,

Sin 35° = AC/AB

⇒ 0.57 = x/5

⇒ x = 0.57 × 5

= 2.85.

The length of the opposite side AC is 2.85 units.

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Answer: x < -46/17

Step-by-step explanation:

To solve the inequality:

1/3x - 1/4(x + 2) > 3x - 4/3

First, we simplify the left-hand side by finding a common denominator:

4(1/3x) - 3/4(x + 2) > 3x - 4/3

4/3x - 3/4x - 9/2 > 3x - 4/3

Next, we simplify the equation:

7/12x - 9/2 > 3x - 4/3

To isolate the variable x on one side of the inequality, we will move all the x terms to the left-hand side and all the constants to the right-hand side:

7/12x - 3x > 9/2 - 4/3

-17/12x > 23/6

Finally, we can solve for x by dividing both sides by -17/12, remembering to reverse the inequality because we are dividing by a negative number:

x < (23/6) ÷ (-17/12)

x < -46/17

Therefore, the solution to the inequality is:

x < -46/17

Nicolas drinks 3/2 liters of water in total - 1/3 liters of water in the morning, 1/2 liter of water at lunch, and 2/3 liter of water during basketball practice.

Nicolas drinks to third liter of water in the morning, which is 1/3 liters of water. At lunchtime, he drinks 1/2 litre of water. During basketball practice, he drinks another 2/3 liter of water.

To find the total amount of water that Nicolas drinks, we need to add these quantities together:

Total amount of water = 1/3 + 1/2 + 2/3

To add these fractions, we need to find a common denominator, which is 6 in this case. We can convert each fraction to have a denominator of 6 as follows:

1/3 = 2/6

1/2 = 3/6

2/3 = 4/6

Now we can add the fractions with the same denominator:

Total amount of water = 2/6 + 3/6 + 4/6

Total amount of water = 9/6

We can simplify this fraction by dividing both the numerator and denominator by 3:

Total amount of water = 3/2

Therefore, Nicolas drinks 3/2 litres of water in total.

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84500 reams of paper are the total amount the two companies sell in the past five years.

65500 is the amount that Company B performed better than company A.

A company can be defined as the part in which the main aim or goal is to earn a profit. This was to generate the income that they will be having in the firm. There are various employees that are present in the company and work towards a common goal.

The Amount that is made by company A is

[tex]7.5 \times 10000[/tex]

[tex]=75000[/tex]

The amount of paper manufactured by company B is

[tex]= 9.5 \times 1000[/tex]

[tex]= 9500[/tex]

A) The total that is made by both companies in 5 years will be

[tex]= \text{Company A + Company B}[/tex]

[tex]= 75000 + 95000[/tex]

[tex]= 84500[/tex]

B) Company B made better products as compared to Company A

[tex]= \text{Company B - Company A}[/tex]

[tex]=75000 - 9500[/tex]

[tex]=65500[/tex]

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Answer:

Step-by-step explanation:

You want the sum and difference of 7.5×10^4 and 9.5×10^3.

Numbers are most conveniently added or subtracted in scientific notation when the multipliers have the same exponent. For this we can rewrite Company B's volume as ...

  9.5×10^3 = 0.95×10^4

  total sales = 7.5×10^4 + 0.95×10^4 = 8.45×10^4 = 84,500

  difference in sales = A -B = 7.5×10^4 -0.95×10^4 = 6.55×10^4 = 65,500

__

Additional comment

You can enter the numbers "as is" in a calculator or spreadsheet and format the output in whatever form you need.

The volume is 63.717 cubic units

The limits of integration for rho are 0 and 4 cos phi, since the sphere has radius 4 cos phi. The limits for phi are π/4 and π/2, since we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of a point. Finally, the limits for theta are 0 and 2π, since theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.

Thus, the volume of the region is given by:

V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos phi) ρ² sin phi dρ dphi dtheta

Simplifying the integral using basic calculus, we get:

V = 8 x (64/3 - 16/3√2π) = 63.717

Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere rho = 4 cos phi is 8(64/3 - 16/3√2π), which is an exact answer using π as needed.

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 The 32 ways to get a five-card combination containing two jacks and three aces.

(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.

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Answer:

Cost price (CP) = Rs20

% Profit = 10%

Selling price (SP) = y

By formula:

% Profit = (Profit/CP) x 100%

But Profit= SP - CP

Therefore;

% Profit = [(SP-CP)/C.P)] x 100%

Substituting, we have:

10% = [(y-20)/20] x 100%

10/100 = (y-20)/20

1/10 = (y-20)/20

1 = (y-20)/2

Cross multiply

y - 20 = 2

y = 2 + 20

y = 22

Therefore, the Sale price is Rs 22

Answer:

Step-by-step explanation:

xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc

First, we need to find the value of g(pi/2):

g(pi/2) = cos(pi/2) = 0

Now we can substitute this value into f(x):

f(g(pi/2)) = f(0) = sin(0) = 0

Therefore, f(g(pi/2)) = 0.

Based on the information, the pollster's conclusion makes sense.

To know if the pollster is right with his conclusion we must perform the following operation.

In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.

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The triangles are similar by the AA similarity criterion since they have two pairs of congruent angles (41° and 109°, and 30°). Therefore, the answer is B. AA.

A triangle is a polygon that has three sides, three vertices, and three angles. It is the simplest polygon in Euclidean geometry and one of the most studied shapes in mathematics. The sum of the three angles in a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the other two sides. There are many different types of triangles, including equilateral triangles (where all sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where no sides are equal). Triangles are used in many areas of mathematics and science, including trigonometry, geometry, and physics.

Here,

To determine whether the two triangles are similar using AA similarity, we need to compare the angles of both triangles.

Triangle 1 has angles 41°, 30°, and 109°.

Triangle 2 has angles 30°, 41°, and 109°.

We see that the two triangles have two pairs of congruent angles, namely 41° and 41°, and 109° and 109°. Therefore, the two triangles are similar by the AA similarity criterion.

Note that the order of the angles does not matter when comparing triangles for similarity.

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The circle graphs which correctly represents the data in the table is "a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent"

The correct answer choice is option B.

Type of Sandwich Number of Customers

Vegetarian 30

Turkey 20

Ham 35

Chicken 15

Total number of customers = 30 + 20 + 35 + 15

= 100

Percentage of each sandwich:

Vegetarian = 30/100 × 100

= 30%

Turkey = 20/100 × 100

= 20%

Ham = 35/100 × 100

= 35%

Chicken = 15/100 × 100

= 15%

Therefore, a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent represents the table.

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Answer:

6 5/6 cups

Step-by-step explanation:

Add.

4 2/3 = 4 4/6

4 4/6 + 2 1/6 gives 6 5/6 cups were used in all.

Hope this helps!

The country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

A medal is a small, flat, and usually round piece of metal that is awarded to individuals or groups as a symbol of recognition or honor for achievement, bravery, or other notable deeds. Medals can be made of various materials, such as gold, silver, bronze, or other alloys, and they often feature intricate designs or engravings that reflect the significance of the award.

According to the circle graph, gold medals make up 20% of the total medals, which means the country won 20% of 150 medals as gold, or 0.2 x 150 = 30 gold medals.

Similarly, silver medals make up 30% of the total medals, which means the country won 30% of 150 medals as silver, or 0.3 x 150 = 45 silver medals.

Finally, bronze medals make up 50% of the total medals, which means the country won 50% of 150 medals as bronze, or 0.5 x 150 = 75 bronze medals.

Therefore, the country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

So the answer is 120.

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The numbers ordered from least to greatest are 0.721, 73/100, and 0.75.

0.75, 0.721, 73/100

we can convert the fraction 73/100 to a decimal by dividing 73 by 100, which gives us 0.73.

0.721 < 0.73 < 0.75

"Least" is a mathematical term used to refer to the smallest value in a given set of numbers or a range of values. It is the opposite of the term "greatest," which refers to the largest value in the set. To find the least value in a set of numbers, you can sort them in ascending order and select the first or smallest number. Alternatively, you can use mathematical formulas or functions such as the minimum function to determine the least value.

In algebra, finding the least common multiple (LCM) or least common denominator (LCD) involves identifying the smallest multiple or denominator that two or more numbers or expressions have in common. This is essential in simplifying and solving complex equations and expressions. In geometry, the least distance between two points is the straight line or path that connects them and is the shortest possible route between them. This concept is fundamental in navigation and optimization problems.

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The answer is d please

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

We have to find the smallest possible factor of 15 and multiple of 3.

The smallest factor of any positive integer is 1.

The smallest multiple of any positive integer is the integer itself. So the smallest multiple of 3 would be 3 itself.

[tex]1 * 3 = 3[/tex]

And 3 is the answer.

Answer:

Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck​

Step-by-step explanation:

Let's start by subtracting the base fee from the total cost:

$143.43 - $16.95 = $126.48

Now, we can divide the remaining cost by the cost per mile:

$126.48 ÷ $0.93/mile ≈ 136 miles

Therefore, Stacy drove the truck for approximately 136 miles.

The area of the figure  is option (C) 61.12 in².

The area of a triangIe is the region encIosed within the sides of the triangIe. The area of a triangIe varies from one triangIe to another depending on the Iength of the sides and the internaI angIes. The area of a triangIe is expressed in square units, Iike, m2, cm2, in2, and so on.

The area of a circIe is the amount of space encIosed within the boundary of a circIe. The region within the boundary of the circIe is the area occupied by the circIe. It may aIso be referred to as the totaI number of square units inside that circIe. Area of CircIe = πr2 or πd2/4 in square units, where

(Pi) π = 22/7 or 3.14.

r = radius of the circIe

d = diameter of the circIe

Pi (π) is the ratio of circumference to diameter of any circIe. It is a speciaI mathematicaI constant.

Area of triangIe = ½ x B x H

Given Height = 8 in

Given Breath = 9 in

Area of TriangIe = ½ x 8 x 9 = 36 in²

Area of haIf circIe = ½ (pi x r²)

= ½ (3.14 x 16)

= (½ x 50.24) in²

= 25.12 in²

Area of the figure wiII be 36 in² + 25.12 in² = 61.12 in²

Option C wiII be the correct option.

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The area of the figure will be 36 in² + 25.12 in² = 61.12 in². Option C will be the correct option.

What is the Area of CircIe?

The area of a circIe is the amount of space enclosed within the boundary of a circIe. The region within the boundary of the circIe is the area occupied by the circIe. It may aIso be referred to as the total number of square units inside that circle.

Area of CircIe = πr2 or πd2/4 in square units, where

(Pi) π = 22/7 or 3.14.

r = radius of the circIe

d = diameter of the circIe

Pi (π) is the ratio of circumference to diameter of any circIe. It is a speciaI mathematicaI constant.

Area of triangle = ½ x B x H

Given Height = 8 in

Given Breath = 9 in

Area of TriangIe = ½ x 8 x 9 = 36 in²

Area of haIf circIe = ½ (pi x r²)

= ½ (3.14 x 16)

= (½ x 50.24) in²

= 25.12 in²

Therefore, Area of the figure will be 36 in² + 25.12 in² = 61.12 in²

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Based on the information in the diagram of circle P, the magnitude of the missing angle are as follows;

m∠BPC = 80 degrees.

m∠ADC = 205 degrees.

In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.

Based on the information provided about circle P, the central angle of circle P is represented by m∠BPC and the measure of arc BC is equals to 80 degrees. Therefore, the magnitude of angle BPC is given by:

m∠BPC = 80 degrees.

Since m∠A is an inscribed angle, its magnitude can be calculated as follows;

m∠A = 1/2(m∠BPC)

m∠A = 1/2(80)

m∠A = 40 degrees.

For the magnitude of m∠ADC, we have:

m∠ADC = 360 - (80 + 75)

m∠ADC = 360 - 155

m∠ADC = 205 degrees.

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Question 7. C (rectangular pyramid)

Question 8. 17 cm

Answer:

Question 7:C rectangular pyramid

Question 8: C 120 in

A=2(wl+hl+hw)=2·(10·2+5·2+5·10)=160

Step-by-step explanation: