A segment of the graph of the function f(x) = -2x - 2 is shown.

Please guys

Using Pythagorean's theorem we can see that the measure of the other leg of the right triangle is 17.89 cm

By Pythagorean's theorem, we know that the sum of the squares of the legs is equal to the square of the hypotenuse.

Then if the other leg has a length x, we can write the equation:

[tex]x^2 + 2^2 = 18^2[/tex]

Solving for x we get:

[tex]x = \sqrt{(18^2 - 2^2)}[/tex]

Solving that square root we will get:

x = 17.89 cm

That is the measure of the other leg of the right triangle.

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Answer:

Step-by-step explanation:

find fraction and multiply by the full length of arc which is circumference

i.e.  [tex]\frac{part circle}{whole circle} * 2\pi r[/tex]

=[tex]\frac{45}{360} *2\pi 1[/tex]                      reduce fraction

=[tex]\frac{1}{4} \pi[/tex]

That day the number of adults was 95 and the number of children was 38

Let's define the variables:

x = number of adults.

y = number of children.

We know that 133 people used the public swimming pool. then we can write:

x + y = 133

We also know that the receipts for admission totaled 270.75, then we can write other equation as:

2.25x + 1.5y = 270.75

Then the system of equations is:

x + y = 133

2.25x + 1.5y = 270.75

In the first equation we can isolate x to get:

y = 133 - x

Now replace that in the other equation to get:

2.25x + 1.5*(133 - x) = 270.75

0.75x + 199.5 = 270.75

0.75x = 270.75 - 199.5

x = 71.25/0.75 = 95

Then the value of y is:

y = 133 - 95 = 38

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Answer:

Step-by-step explanation:

The bank paid for somthing for David. Now Davids Bank Account is in the negitve of $52. Now he owes the bank money.

if you take how much money david had

and subtact it with 95 it will equal up to $-52

________________________________________________________

Answer:

the picture ain't clear.

Solving multi-step equations involves systematically isolating the variable through algebraic operations. In terms of the 'digital puzzle', it would require the matching of solved multi-step equations with their solutions, providing a practical method of practicing algebra skills.

Based on your question, it appears you are working on a multi-step equation puzzle. In solving multi-step equations, it is important to systematically isolate the variable. For example, if you have a multi-step equation like 3x + 2 = 14, you would first subtract 2 from both sides and then divide by 3 to get x = 4, which is the solution. Each step involves an algebraic operation, and the aim is to simplify the equation to reach your final answer.

The mentioned 'digital puzzle' is most likely an interactive activity where you have to match these multi-step equations with their corresponding solutions. Simply solve each equation and drag the solution to its corresponding equation. This is a great way to practice algebra skills.

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Step-by-step explanation:

To simplify the given expression:

2[3(4^2+1)]-2^3

First, we evaluate the exponent:

4^2 = 4 * 4 = 16

Now we can substitute this value back into the original expression:

2[3(16+1)]-2^3

Next, we perform the addition inside the parentheses:

16 + 1 = 17

Substituting this back into the expression:

2[3(17)]-2^3

Then, we perform the multiplication inside the square brackets:

3 * 17 = 51

Substituting this back into the expression:

2[51]-2^3

Next, we perform the exponent:

2^3 = 2 * 2 * 2 = 8

Substituting this back into the expression:

2[51]-8

Finally, we perform the remaining multiplication:

2 * 51 = 102

Substituting this back into the expression:

102 - 8

Now we can perform the subtraction:

102 - 8 = 94

So, the simplified form of the given expression is 94.

The system of equations 5x - 3y = -26 and x + 2y + 1 = 2 can be solved using the substitution method. The solution of the system of equations is x = -8.2 and y = -5.

An equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equals sign (=). Equations are used to describe relationships between different quantities, and to solve problems involving those quantities. Equations may be written in words, symbols, or both. They can be used to solve problems in science, engineering, economics, and other fields.

The system of equations can be solved using substitution method or addition method. In this solution, we will use the substitution method.

Substitution Method:

Step 1: Solve one of the equations for either x or y.

Let us solve the first equation for x.

5x - 3y = -26

5x = -3y - 26

x = (-3y - 26)/5

Step 2: Substitute the expression for x in the second equation.

x + 2y + 1 = 2

(-3y - 26)/5 + 2y + 1 = 2

Step 3: Solve the equation for y.

(-3y - 26)/5 + 2y + 1 = 2

-3y/5 - 26/5 + 2y + 1 = 2

2y - 3y/5 - 26/5 + 1 = 2

-y/5 - 26/5 + 1 = 2

y/5 + 26/5 - 1 = -2

y/5 + 25/5 = -1

y = -5

Step 4: Substitute the value of y in either of the equations to calculate the value of x.

5x - 3(-5) = -26

5x + 15 = -26

5x = -41

x = -41/5

x = -8.2

Therefore, the solution of the system of equations is x = -8.2 and y = -5.

Conclusion:

The system of equations 5x - 3y = -26 and x + 2y + 1 = 2 can be solved using the substitution method. The solution of the system of equations is x = -8.2 and y = -5.

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The age of Savannah is 11 years old.

The age of Savannah is calculated as follows;

Let x be the age of Gianna

Savannah's age can be expressed as x + 2

The product of their ages is 99, so we can set up the equation;

x(x + 2) = 99

x² + 2x = 99

x² + 2x - 99 = 0

Factorize the quadratic equation as follows;

x² + 11x - 9x - 99 = 0

(x + 11)(x - 9) = 0

x = -11 or 9

ignore the negative solution.

So, Gianna is 9 years old, which means that Savannah is 9 + 2 = 11 years old.

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The age of Alvin is 66 years. Then the age of Elga will be 22 years.

Given that:

Alvin's age is three times Elga's age. The sum of their ages is 88.

Let 'x' be the age of Alvin and 'y' be the age of Elga. Then the equations are given as,

x = 3y                      ...(1)

x + y = 88                ...(2)

From equations (1) and (2), then we have

3y + y = 88

4y = 88

y = 22

Then the value of 'x' is calculated as,

x = 3 × 22

x = 66

The age of Alvin is 66 years. Then the age of Elga will be 22 years.

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The options that complete the statements are:

The converse Pythagoras theorem states that If the square of a side is equal to the sum of the square of the other two sides, then the triangle must be a right-angled triangle.

Thus, given ABC with side lengths a, b, c.

where a² + b² = c²

Then c must be the side opposite a right angle and ABC must be a right triangle.

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Where the above conditions are given, the correct graph is "a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44" (Option A)

We must examine the data to choose the best graph for this case. In this scenario, the toppings have a link with the amount of clients that choose each flavor.

We may conclude that the best choice is A based on the amount of persons who like each topping in the order in which the table organizes them.

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The equation of the cost of renting a bicycle given by Krissy is non-proportional.

Here we see that the function Krissy wrote was

y = 5x + 15.

A function is called a proportional function if y/x is some fixed constant. This means, rearranging the equation should give us

y/x = k, where k is some constant.

Here we have,

y = 5x + 15

Dividing both sides by x will give us

y/x = 5 + 15/x

Now, clearly RHS is not a constant as it has a variable x present. Hence the function is non-proportional.

Another way to check the proportionality of a function is to check whether the function is in the form of

y = cx, where c is a constant. Here, there should not be added or subtracted constant with x. On the concerned equation, RHS had an additional constant of + 15.

Hence, the equation given by Krissy is a non-proportional function.

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(Image Attached)

A t-distribution with 8 degrees of freedom has been graphed, and the shaded region under the curve to the right of t0.2 represents the probability of obtaining a t-value greater than t0.2. The area of this region is 0.2, which means there is a 20% probability of getting a t-value greater than t0.2 in this distribution.

1. Distribution: In this context, it refers to a statistical distribution, which is a function describing the probability of different outcomes in an experiment. Here, we have a t-distribution with 8 degrees of freedom.

2. Graphed: This means that the distribution is represented visually as a curve on a graph, with the x-axis representing the t-values and the y-axis representing their probabilities.

3. Region under the curve: In a probability distribution graph, the region under the curve represents the probabilities associated with different t-values. The area of this region corresponds to the probability of a particular outcome or range of outcomes.

4. Area of this region: In the given scenario, the shaded region under the curve to the right of t0.2 has an area of 0.2, indicating that the probability of obtaining a t-value greater than t0.2 is 0.2, or 20%.

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The formula for the volume of a cube is V = a³, where a is the length of one of its sides or edges

If the base, height and width of a cube are all 1/3, then the volume of the cube is:

V = (1/3)³

V = 1/27

So, the volume of the cube is 1/27 cubic units.

Colin purchases a package of pasta with 8 2/3 cups of spaghetti inside. He makes dinner with 2 1/2 cups. Pasta is down to 6 1/6 cups for Colin.

To find out how much pasta is left, we need to subtract the amount used from the total amount of pasta:

8 2/3 cups - 2 1/2 cups

First, we need to convert the mixed numbers to improper fractions, which will make it easier to subtract them:

8 2/3 = (8 x 3 + 2) / 3 = 26/3

2 1/2 = (2 x 2 + 1) / 2 = 5/2

Now we can subtract:

26/3 - 5/2

We must identify a common denominator in order to subtract fractions with various numerators. Since 3 and 2 have a least common denominator of 6, we can convert both fractions to have a denominator of 6:

26/3 = (26/3) x (2/2) = 52/6

5/2 = (5/2) x (3/3) = 15/6

Now we can subtract:

52/6 - 15/6 = 37/6

Therefore, Colin has 6 1/6 cups of pasta left.

When the numerator (the top number) exceeds the denominator (the bottom number), the fraction is said to be improper. This means that the fraction represents a value greater than one, and is often expressed as a mixed number (a whole number and a proper fraction).

Improper fractions are commonly used in math and can represent values in a variety of contexts, such as in measurements or in calculations. They can be added, subtracted, multiplied, and divided just like any other fraction. It is important to know how to convert improper fractions to mixed numbers and vice versa, as well as how to perform operations with them, in order to effectively solve mathematical problems.

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The graph of the inequality expression 10x+5y < -4 is attached

From the question, we have the following parameters that can be used in our computation:

10x+5y-4

Express properly

So, we have

10x+5y < -4

Next, we plot the graph using a graphing tool

The graph is added as an attacment

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Let a number be 'x'

∴ 1 less than twice x = 2x - 1

When you rewrite an addition or subtraction problem using the Distributive Property, you have to factor out both values by a common factor, usually the GCF.

This process involves identifying the common factor (the greatest common factor, or GCF) of the terms and then applying the Distributive Property to rewrite the expression. This common factor can be the greatest common factor (GCF) if it exists, but it does not have to be. The goal is to find a factor that is common to both terms, so that it can be factored out and the expression can be simplified.For example, consider the expression 6 + 8. We can rewrite this using the distributive property by factoring out 2, which is a common factor of both 6 and 8:6 + 8 = 2(3) + 2(4)Then, we can simplify the expression by adding the like terms:2(3) + 2(4) = 6 + 8 = 14Note that in this example, we factored out the common factor 2, which is not the GCF of 6 and 8 (the GCF is 2). However, factoring out 2 allowed us to simplify the expression using the distributive property.

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3.628 fluid ounces will not fit in the pitcher.

We are given the volume of water in a 2-liter bottle and the volume of a 2-quart pitcher. However, the units of measurement are different.

Hence, we need to convert one or both of the volumes to the same units before we can compare them. Use unit conversion factors to convert liters to fluid ounces and quarts to fluid ounces.

Here we have

You pour water from a 2-liter bottle into a 2-quart pitcher without spilling

One liter is equivalent to 33.814 fluid ounces, while one quart is equivalent to 32 fluid ounces.

Therefore, we have:

2 liters = 67.628 fluid ounces

2 quarts = 64 fluid ounces

Since we cannot spill any water, we know that the maximum amount of water that can fit in the pitcher is 64 fluid ounces.

To determine how many ounces will not fit in the pitcher, subtract the amount of water that will fit in the pitcher from the total amount of water in the 2- liter bottle.

This gives us:

67.628 - 64 = 3.628 fluid ounces

Therefore,

3.628 fluid ounces will not fit in the pitcher.

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Here are three values that would make the inequality 7n ≤ 21 true are found out to be n = 0, n = 1 and n = 3.

The inequality 7n ≤ 21 means that the product of 7 and n is less than or equal to 21. To make this inequality true, we need to find values of n that satisfy this condition.

If we substitute n = 0, we get 7(0) = 0, which is less than or equal to 21. Therefore, the inequality is true for n = 0.

If we substitute n = 1, we get 7(1) = 7, which is less than or equal to 21. Therefore, the inequality is true for n = 1.

If we substitute n = 3, we get 7(3) = 21, which is equal to 21. Since 21 is also less than or equal to 21, the inequality is true for n = 3.

Note that there are many other values of n that would also make the inequality true, such as any value of n less than or equal to 3.

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He will have 16 meters of border left over after covering all four walls.

To calculate the total length of the walls, we add the lengths of each wall:

16m + 12m + 20m + 16m = 64m

So, Christan needs to cover 64 meters of walls with the wallpaper border.

If he has 80 meters of border available, then he should have enough to cover all four walls, and he will have some left over.

To calculate how much he will have left over, we subtract the total length of the walls from the length of the border:

80m - 64m = 16m

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Thus, the correct options are C, D, and E.

Given: Anna bought 8 tetras and 2 rainbow fish for her aquarium.

To Find: Which option is correct?

Solution: Let's say that the price of tetras is x, which means the price of a rainbow fish will be (x + 6).

Here, we get the equation,

8x +2(x + 6)=37

Now, after simplifying the above equation, we get

10x + 12 =37

By adding -12 on both sides of the equation, we get

10x = 37 - 12 =25

Now, we will divide the equation with 10

x = 25/10

After simplifying the equation, we get

x = 5/2 = 2.5

So, the cost of a tetra will be $2.5, and the cost of a rainbow fist will be $2.5 + $6 = $8.5

Here, option B is false because the cost of each rainbow fish is greater by $6, and here 6 is only taken once.

Option A is false because 4(2.5) is not equal to 8.5.

Option E is true because 37 - 8.5 = 28.5.

Option D is true because the equation that is being used has only one difference which is the selection of variable.

Option C is true because 5(2.5) + 8.5 = 12.5 + 8.5 = 21.

Thus, the correct options are C, D, and E.

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The bases of both the triangles are 15 and 5 units respectively.

Given are right triangles we need to find the bases of the triangles,

Using the trigonometric ratios,

1) Let the base be b,

We know that the tangent of an angle is the ratio of the perpendicular side to the base.

So,

Tan 60° = 15√3/b

b = 15√3/√3

b = 15

Therefore the base of the first triangle is 15 units.

Similarly,

2) The cosine of an angle of rt. triangle is the ratio base to the hypotenuse.

So,

Cos 45° = m/5√2

1/√2 = m/5√2

m/5 = 1

m = 5

Therefore the base of the first triangle is 5 units.

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The rate of decrease is slower between points B and C compared to the rate of decrease between points A and B.

If you consider the points A(2013; 0.94), B(2015; 0.93), and C(2020; 0.91), calculate the slopes of lines AB and BC and interpret the results.

In order to calculate the slopes of lines AB and BC, you can use the slope formula:

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

For line AB, use points A(2013; 0.94) and B(2015; 0.93):

Slope_AB = (0.93 - 0.94) / (2015 - 2013)

Slope_AB = (-0.01) / (2)

Slope_AB = -0.005

For line BC, use points B(2015; 0.93) and C(2020; 0.91):

Slope_BC = (0.91 - 0.93) / (2020 - 2015)

Slope_BC = (-0.02) / (5)

Slope_BC = -0.004

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The ratio of density of cylinder A to cylinder is 8 : 49.

The ratio of the density of the two cylinders is calculated as follows;

The formula for the density of the cylinders is given as;

density = m / (πr²h)

For cylinder A and B;

height = h = h_B = h

mass = m, m_B = 2m_A = 2m

radius, = r, r_B = 4/7r_A = 4/7r

Density of cylinder A = m / (πr²h)

Density of cylinder B = 2m/(π(4/7r)²h = 2m/π16r²h/49  = (2m x 49)/π16r²h

Ratio of the two densities is calculated as;

A/B =  m / (πr²h)     x       π16r²h / (2m x 49)

= 16/(2 x 49)

= 8/49

= 8 : 49

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Answer:

Liam has $12.

Step-by-step explanation:

Since Drew has $18 and that is $6 more than Liam's amount of money, you would subtract 6 from 18.

18-6=12

Hence, Liam has $12.

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Answer:

The check Bob wrote was $134.

Step-by-step explanation:

110 + 24 = 134

110 - 134 = (-24)

Hope this helps!

Answer:

50

Step-by-step explanation:

A person travels to work at an average speed of 40 mph, and returns home at 60 mph. the average speed for the entire trip is 48 mph.

To find the average speed for the entire trip, we need to use the formula:

average speed = total distance / total time

Let's assume that the distance to work is d.

The time it takes to travel to work is:

time = distance / speed = d / 40

The time it takes to return home is:

time = distance / speed = d / 60

The total distance for the round trip is:

total distance = d + d = 2d

The total time for the round trip is:

total time = d/40 + d/60

We can simplify the total time by finding a common denominator:

total time = (3d/120) + (2d/120) = 5d/120 = d/24

Now we can plug in the values for total distance and total time:

average speed = (2d) / (d/24) = 48 mph

Therefore, the average speed for the entire trip is 48 mph.

To find the average speed for the entire trip, we can use the harmonic mean formula for two rates: average speed = (2 * speed1 * speed2) / (speed1 + speed2). In this case, speed1 is 40 mph (to work) and speed2 is 60 mph (returning home).

Using the formula: average speed = (2 * 40 * 60) / (40 + 60) = (4800) / (100) = 48 mph.

So, the average speed for the entire trip is 48 mph.

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When the sample size is small and the population distribution is not normal, the mean is a biased estimate.

Nonetheless, the bias of the mean reduces as the sample size grows, making it a more trustworthy estimator. As a result, the mean is the biased estimator whose bias will decrease as the sample size increases.

Increasing the sample size has no impact on the bias of the median, standard deviation, and range estimators since they are non-biased estimators.

These estimators may, however, be made more precise and accurate by increasing the sample size, which increases their dependability for predicting population parameters.

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Complete question:

Which biased estimator will have a reduced bias based on increased sample size? mean median standard deviation range

The probability that the customer will select two tickets with discounts of $3 and $5 is $1/9 or approximately $0.111.

The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It represents the probability of an event happening. A number between 0 and 1, where 0 denotes impossibility and 1 denotes certainty, is used to symbolize it. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. Numerous disciplines, including science, engineering, finance, economics, and social sciences, to mention a few, make extensive use of probability theory.

Since the customer selects a ticket, replaces it, and selects another ticket, the two selections are independent events. The probability of selecting a $3 discount ticket on the first meal is $1/3, and the probability of selecting a $5 discount ticket on the second meal is also $1/3.Therefore, the probability of selecting both a $3 and a $5 discount ticket is:

[tex]\frac{1}{3} . \frac{1}{3} = \frac{1}{9}[/tex]

​

So the probability that the customer will select two tickets with discounts of $3 and $5 is $1/9 or approximately $0.111.

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