An isosceles triangle has a perimeter of 19 inches. A leg is 2 inches longer than the base. How long is the
base?

The weights of the three parts are 200g, 120g, and 160g, respectively, in the ratio of 5:3:4.

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

To divide 480g in the ratio 5:3:4, we need to divide the total amount into 3 parts (corresponding to the three parts of the ratio), where the first part is 5/12 of the total, the second part is 3/12 (or simplified, 1/4) of the total, and the third part is 4/12 (or simplified, 1/3) of the total.

To find the weight of the first part (in the ratio of 5), we need to multiply the total weight by the fraction representing the first part of the ratio:

5/12 * 480g = 200g

To find the weight of the second part (in the ratio of 3), we need to multiply the total weight by the fraction representing the second part of the ratio:

1/4 * 480g = 120g

To find the weight of the third part (in the ratio of 4), we need to multiply the total weight by the fraction representing the third part of the ratio:

1/3 * 480g = 160g

Therefore, the weights of the three parts are 200g, 120g, and 160g, respectively, in the ratio of 5:3:4.

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Answer:

length of rectangular prism: 9 feet

width of rectangular prism: 9 feet

Step-by-step explanation:

volume= length x width x height

567/7=81

Since 81 cubic feet squared is the area of the base; the square bottom, you will need to find the square root of 81 which is 9 since 9 times 9 equals 81.

The w-intercept of the line of fit is 5.05, and its meaning in terms of the scenario is that a puppy who is just born is predicted to weigh 5.05 ounces.

The intercepts are defined as an intercept that is located at the axes of the graph, which are the location or coordinates from where the line crosses.

The w-intercept of the line of fit is the value of w when d = 0, which means the weight of a puppy when it is born.

According to the equation w = 5.05 + 0.3d, when d = 0, we have:

w = 5.05 + 0.3(0) = 5.05

Therefore, the w-intercept of the line of fit is 5.05,

This means in terms of the scenario that a puppy who is just born is predicted to weigh 5.05 ounces.

Hence, the correct answer is B.

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From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer for the graph.

Calculus uses a function's derivative to determine whether a function is rising or decreasing at various intervals in a specific domain. Given a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We observe that the function of f approaches to 0 as it moves towards infinity. Thus, it is a decreasing function.

From the given options, option 1 depicts a decreasing function. Hence, option 1 is the correct answer.

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Answer: the image didnt send with this try reposting

Step-by-step explanation:

this is a little funny out of context tho, best of luck be upon you

The location of A ' given the rotation about the origin and the xy coordinate plane is D. In Quadrant IV.

To rotate a point 180° about the origin, we switch the signs of both coordinates. For instance, if you have ( x, y ) rotated, then it becomes ( - x ,  - y ).

So, if A is located at (-4, 3), then A' is located at (4, -3).

The point A' is located in Quadrant IV, because it has a positive x-coordinate and a negative y-coordinate, which is the characteristic of points in this quadrant.

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The most effective action that Fatimah can take to reduce the reservoir's amount of water loss is to install an evaporation control system.

What is amount?

Amount is a term used to refer to the quantity or magnitude of something, typically in financial or numerical terms. It can refer to physical items such as money, goods, or services, as well as abstract concepts such as time, distance, or energy. The amount of something is usually determined by measuring, counting, or weighing it.

Evaporation is a major source of water loss in arid regions, as the dry air quickly absorbs the moisture from the reservoir's surface. By installing an evaporation control system, Fatimah can reduce the amount of water lost to evaporation by using a variety of strategies. These strategies can include the use of an impermeable membrane to cover the reservoir's surface, the installation of windbreaks to reduce the speed of the wind over the water, and the use of chemicals to reduce the rate of evaporation. All of these strategies can be used to drastically reduce the amount of water lost to evaporation.

The installation of an evaporation control system can also be relatively inexpensive compared to other solutions. For instance, compared to installing a new water pump system or rerouting water to the reservoir, installing an evaporation control system can be done quickly and at a lower cost. This makes it a more suitable solution for Fatimah's limited budget.

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The value οf h is apprοximately 2.83. Sο the answer is (A) 2.

Expοnential expressiοns invοlve a base number raised tο a pοwer οr expοnent. The expοnent indicates hοw many times the base number shοuld be multiplied by itself.

We can simplify the expressiοn [tex]9(2)^{5x+10}[/tex] as follows:

[tex]9(2)^{5x+10} = 9(32)^{x+10}[/tex]

We can then rewrite this expression as [tex]9(h)^{x+2},[/tex] where h is a variable:

[tex]9(h)^{x+2} = 9(32)^{x+10}[/tex]

Comparing the expοnents of h and 32, we can see that h = [tex]2^{(5/2)}[/tex], or h = 2 * sqrt(2) = 2.83 (rounded to twο decimal places).

Hence, the value οf h is approximately 2.83. So the answer is (A) 2.

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Answer:

= 0.375

Step-by-step explanation:

then 3/8 to it decimal fraction

[tex] \frac{3}{8} \\ = 0.375[/tex]

Answer:

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, we can consider the distance from home to Best Buy as the hypotenuse, and the distance traveled west and south as the other two sides.

Let's call the distance from home to Best Buy "x". Then, using the Pythagorean theorem:

x^2 = (distance south)^2 + (distance west)^2

We know that the distance west is 5 miles, and the distance home is 25 miles. We don't know the distance south, so let's call that "y".

Then we have:

x^2 = y^2 + 5^2

25^2 = y^2 + 5^2

Solving for y, we get:

y^2 = 25^2 - 5^2

y^2 = 600

y = sqrt(600)

y = 24.49 (rounded to two decimal places)

Now we can plug in y to find x:

x^2 = y^2 + 5^2

x^2 = 24.49^2 + 5^2

x^2 = 625.12

x = sqrt(625.12)

x = 25.00 (rounded to two decimal places)

Therefore, the distance from home to Best Buy is approximately 25 miles.

Step-by-step explanation:

The sectors of the circle graph is solved and the field trip with the measure of section is

Aquarium = 90°

Science Museum = 144°

Botanical Gardens = 54°

Planetarium = 72°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

θ/360 * πr²

where;

θ is the central angle of the sector

r is radius

Now, looking at the given options we can say that the only one that represents the area of the sector is;

A = n/360 * πr²

where n is the central angle of the sector

Given data ,

Let the area occupied by the circle be represented as A

Now , the values of A are

Let the field trip be represented as y

Let the number of votes be represented as x

y = { Aquarium , Science Museum , Botanical Gardens , Planetarium }

x = { 30 , 48 , 18 , 24 }

Now , the total sector angle occupied by field trip is T = 120°

x₁ = ( 30/120 ) x 360

x₁ = ( 1/4 ) x 360

x₁ = 90°

when x₂ = 48

x₂ = ( 48/120 ) x 360

x₂ = ( 0.4 ) x 360

x₂ = 144°

when x₃ = 18

x₃ = ( 18/120 ) x 360

x₃ = ( 0.15 ) x 360

x₃ = 54°

when x₄ = 18

x₄ = ( 24/120 ) x 360

x₄ = ( 0.2 ) x 360

x₄ = 72°

Hence , the measures of the section of circle is solved

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Answer: 31

Step-by-step explanation:

Answer:

depends

Step-by-step explanation:

?

In answering the question above, the solution is As a result, when x gets function closer to infinity, the function's limit is equal to 0.

Mathematicians investigate the relationships between numbers, equations, and related structures, as well as the locations of forms and possible placements for these items. A set of inputs and their corresponding outputs are referred to as a "function" in this context. If each input results in a single, unique output, the relationship between the inputs and outputs is known as a function. Each function has its own domain, codomain, or scope. A common way to denote functions is with the letter f. (x). is an x for entry. One-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The idea of dominating words can be used to solve this constraint. We see that the denominator x2+8 grows significantly greater than the numerator x-6 as x goes to infinity, therefore we may disregard the smaller component in the numerator and denominator.

As a result, the phrase may be simplified as follows:

Limit x (x - 6) / (x2 + 8) goes to infinity

x / (x2) limit x approaches to infinity

= limit x approaches to infinity 1 / limit x

= 0

As a result, when x gets closer to infinity, the function's limit is equal to 0.

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Answer:

15£

Step-by-step explanation:

if 1£=2$

then30$=30/2

15£

According to the graphs, the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia (option A).

To select an appropriate conclusion that matches the information in the graphs we must carefully analyze the information in the graphs. Additionally, we can read each of the options and check them with the trends shown in the graphs.

In accordance with the above procedure, we can infer that the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia because the Residential real estate graph shows that In 2010 housing was more expensive in Australia than in Spain.

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Answer:

Step-by-step explanation: true

The correct ordered pair for the data is (1, 2), (2, 4), (3, 6), and (4, 8). The correct option is A.

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.

Number of Boxes of Popcorn     Cost ($)

1                                                          2

2                                                         4

3                                                         6  

4                                                         8  

The ordered pair of the data is,

(1, 2),

(2, 4),

(3, 6),

(4, 8),

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Using law of cosine, the distance from the wall at point A is approximately 21.32 feet.

We can use the law of cosines to find the distance from the wall at point A. Let's call this distance d.

In the triangle formed by the center of the merry-go-round, point A, and the point where the merry-go-round touches the wall (let's call this point B), we know that:

Using the law of cosines, we have:

(8)^2 = (42)^2 + (d + 8)^2 - 2(42)(d + 8)cos(130)

Simplifying and solving for d, we get:

d = sqrt[ (8)^2 - (42)^2 cos^2(130) ] - 8

Plugging in the values, we get:

d ≈ 21.32 feet

Therefore, the distance from the wall at point A is approximately 21.32 feet.

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Answer:

Step-by-step explanation:

The equation written in slope-intercept form is: y=3x-2.

Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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This equation works for any number of dogs, as long as the rate remains constant.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

That's correct, Gabby's earnings are directly proportional to the number of dogs she walks. We can use a simple equation to represent this relationship:

Earnings = Rate x Number of Dogs

In this case, Gabby's rate is $10 per dog, so the equation becomes:

Earnings = 10 x Number of Dogs

For example, if Gabby walks 5 dogs, her earnings would be:

Earnings = 10 x 5 = $50

If she walks 8 dogs, her earnings would be:

Earnings = 10 x 8 = $80

And so on.

Therefore, This equation works for any number of dogs, as long as the rate remains constant.

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Using arithmetic operation, the value for time spent on country driving is obtained as 25/44 hour.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Jorge's drive was 3/4 hour, and 2/11 hour of that time was spent on city driving.

To find the time spent on country driving, we can use arithmetic operation of subtraction.

Subtract the time spent on city driving from the total driving time -

Time spent on country driving = Total driving time - Time spent on city driving

= 3/4 hour - 2/11 hour

To subtract these fractions, we need a common denominator.

The smallest number that 4 and 11 both divide into is 44 -

3/4 = 33/44

2/11 = 8/44

So -

Time spent on country driving = 33/44 hour - 8/44 hour

= (33 - 8)/44 hour

= 25/44 hour

Therefore, Jorge spent 25/44 hour driving on country roads.

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Answer:

hi

Step-by-step explanation:

thanks for the poi

The mean temperature increases, the electricity bill decreases.

What is the scatter plots?

A scatter plot is a type of graph that is used to display the relationship between two continuous variables.

To find the correlation coefficient, we first need to plot the data points on a scatter plot. We can use a graphing calculator to do this.

Here are the steps:

The calculator will display the equation of the line of best fit, as well as the correlation coefficient (r).

Using these steps, we get a correlation coefficient of approximately -0.83. Rounded to the nearest hundredth, the correlation coefficient is -0.83.

This negative correlation coefficient indicates a strong negative relationship between mean temperature and electricity bill.

Hence, the mean temperature increases, the electricity bill decreases.

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Hence the value of x from the given diagram is 4.5

The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem, which is a consequence of elementary geometry.

From the diagram shown:

6/8 = x/6

Cross multiply

6*6 = 8x

36 = 8x

x = 36/8

x = 4.5

Hence the value of x from the diagram is 4.5

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The value of probability that they have pulse rates with mean less than 78 beats per min is,

⇒ 0.5948

The term probability refers to the likelihood of an event occurring. 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

Given that;

Mean is 75 beats per min.

And, Standard deviation is, 12.5

Hence, We get;

z = (78 - 75) / 12.5

z = 3/12.5

z = 0.24

Hence, The probability is, 0.5948

Thus, The value of probability that they have pulse rates with mean less than 78 beats per min is,

⇒ 0.5948

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The Required explanation of triangle inequality theorem has been done.

In mathematics, inequalities specify the connection between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol ()" to indicate that two values are not equivalent. But various inequalities are used to compare the values, whether it is less than or larger than.

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides is always greater than the length of the third side. Mathematically, if a, b, and c are the lengths of the sides of a triangle, then a + b > c, b + c > a, and c + a > b.

This theorem is a fundamental principle in geometry and can be used to prove many other theorems related to triangles.

It is also used in everyday life, such as in designing bridges, ensuring the stability of buildings, and determining the shortest distance between two points.

The triangle inequality theorem is a powerful tool in mathematics and is a key concept for anyone studying geometry.

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