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If the hypotenuse is given to the 45 45  90 triangles, the leg of the triangle is calculated after dividing the hypotenuse by [tex]\sqrt{2}[/tex].

The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.

If the leg of the triangle is equal to a, then:

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Answer: x= -2, -3

Step-by-step explanation: Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Yes , she will be able to buy the PlayStation before Marko as she only needs 5 weeks to collect the remaining amount of money.

Cost of PlayStation given = 700 dollars

Amount of money which Rosaline has = 200 dollars

Now, if she has 200 dollars and deposits 100 dollar every week , this means she will be able to collect 700 dollars in 5 weeks of time.

100 dollar = 1 week

therefore, this relation means that  500 dollars = 5  weeks

Hence , she will be able to buy the PlayStation in about 5 weeks from the time she starts collecting the money.

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Answer:

Step-by-step explanation:

The maximum possible number of parasites for the class containing the value 27 is 29

The data for 40 randomly selected honey bee hives on a farm is summarized in the histogram below.

From given histogram we have the classes as:

10 - 15, 15 - 20, 20 - 25, 25 - 30, 30 - 35, 35 - 40, 40 - 45, 45 - 50

To find: the maximum possible number of parasites for the class containing the value 27

The class that contains the value 27 is 25 - 30

Given that each class contains its lower class boundary, but not its upper class boundary.

So, the maximum possible number of parasites for the class containing the value 27 would be 29 as 30 is not part of class 25 - 30

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The logarithmic equation that is equivalent to this exponential equation 2,400=7,500 (10) ^ -x is [tex]x = -log_{10} \frac{8}{25}[/tex]. Option C

from the question we have:

2400 = 7500(10)⁻ˣ

we would have to transform the equation that we have here into the logarithm form.

This is written as:

[tex]\frac{2400}{7500}=10^-^x[/tex]

from here we are to reduce the division

hence we would have:
[tex]10^-^x = \frac{8}{25}[/tex]

-x = log₁₀8/25

then

[tex]x = -log_{10} \frac{8}{25}[/tex]

option c is correct

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Answer:

2/3

Step-by-step explanation:

Slope = rise / run = 2 / 3

Because points A, B, C, and D are collinear (meaning on the same line), the slope for line segment AB is the same as the slope for segment DC.

Answer:

2/3.

Step-by-step explanation:

The 2 triangles are similar so their corresponding sides are in same ratio.

The sides BA and CD are collinear so theire slopes are the same.

Slope of BA = rise/run = 2/3 so slope of DC is also 2/3.

The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

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The graph of equation is in image.

When a linear equation is graphed, it always results in a straight line because each term has an exponent of 1. This is why it is referred to as a "linear equation."

There are linear equations with one and two variables, respectively.

Given equations

2x + 3y = 5

4x - 5y = -1

For equation 1

2x + 3y = 5

The table of values appears as follows

x    1     -2    4

y    1      3    -1

Coordinates for equation 2

4x - 5y = -1

The table of values as thus

x    1     2    -4

y    1     1.8   -3

And the intersection point of equation is (1, 1)

Hence the graph of equation is intersecting at (1, 1).

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The solution for each system of equations is given as follows:

1) x = -4, y = -8.

2) x = 5, y = -1.

3) x = -7, y = 2.

4) No solution.

5) x = 2, y = -6.

6) x = -3, y = 4.

The system of equations are solved using the elimination method, writing  one variable as a function of another, replacing in the other equation, and then obtaining each variable.

For item 1, we eliminate x, as follows:

x = 12 + 2y.

Hence the solution for y is obtained as follows:

5(12 + 2y) + 3y = -44

60 + 10y + 3y = -44

13y = -104

y = -104/13

y = -8.

Then the solution for x is given as follows:

x = 12 + 2y = 12 + 2(-8) = -4.

For item 2, we have that:

y = 19 - 4x.

Hence:

7x - 2(19 - 4x) = 37

7x - 38 + 8x = 37

15x = 75

x = 5.

Hence the solution for y is of:

y = 19 - 4(5) = -1.

For item 3, we can simplify the second equation by two, hence:

-x + y = 9.

y = 9 + x.

Hence:

3x + 8(9 + x) = -5

3x + 72 + 8x = -5

11x = -77

x = -7.

Hence the solution for y is of:

y = 9 - 7 = 2.

For item 4, we have that:

x = 7 + 3y.

Hence:

2(7 + 3y) - 6y = 12

14 + 6y - 6y = 12

0y = -2. (no solution, division by zero).

For item 5, we have that:

y = -2 - 2x.

Hence:

5x + 3(-2 - 2x) = -8

5x - 6 - 6x = -8

-x = -2

x = 2.

Hence the solution for y is of:

y = -2 - 2(2)

y = -6.

For item 6, we simplify the second equation by two, hence:

2x + y = -2

y = -2 - 2x.

Replacing on the first equation, we have that:

2x + 5(-2 - 2x) = 14.

2x - 10 - 10x = 14

-8x = 24

8x = -24

x = -3.

Hence the solution for y is obtained as follows:

y = -2 - 2(-3)

y = -2 + 6

y = 4.

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Probability that the calendar turned to month of May or June is 1/6.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total number of months = 12

Suppose that a calendar is turned.

Probability that the calendar turned to month of May = 1/12

Probability that the calendar turned to month of June = 1/12

Probability that the calendar turned to month of May or June = 1/12 + 1/12

                                                                                                      = 2/12

                                                                                                      = 1/6

Hence the probability that the calendar turned to month of May or June is 1/6.

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The Truth Table in logic gate is  used to specify the output of the logic gate for all possible combinations of the input signals. , it is the breakdown of all the possible truth values returned by the logical expression.

What is Truth Table ?

The truth table is a tabular representation of all combinations of values for inputs and their respective outputs.

It can be called as a mathematical table which shows all possible outcomes that would occur from all the possible scenarios that are considered as  factual.

Truth tables are generally used for the logic problems as in Boolean algebra and electronic circuits.

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Answer:

Step-by-step explanation:

A truth table for a logic gate is the table that specifies the logic value/state of the output of the gate for all possible combinations of the logic states of all inputs.

Let's take the example of the AND gate with two logic inputs A and B and one output Y.

A    B    Y

0    0    0

0    1     0

1     1     1

1    0     0

This is the truth table for the AND gate.

The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

Given that,

We have to find the total surface area of the triangular prism in the given picture.

We know that,

First, we need to calculate the area of ​​the triangle

a = area of triangle

a = 1/2 ×15 cm × 8 cm

a = 60 cm²

Now,

We must determine the three rectangles' areas.

a₁ = 2cm × 17cm

a₁ = 34cm²

a₂ = 2cm × 15cm

a₂ = 30cm²

a₃ = 2cm ×8cm

a₃ = 16cm²

Now, we must multiply the triangle by two and sum all the estimated areas.

a₁ + a₂ + a₃ + 2a =60cm² + 34cm² + 30cm² + 2 × 16cm² = 156cm²

Therefore, The surface area of the triangular prism is 156cm² when the triangle sides are 8cm  and 15 cm rectangle sides are 17cm and 2 cm.

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B. A greater percentage of second-lunch students (39%) eat outside.

From the table above, the percentage second-lunch students who eat outside is calculated as follows:

%= number of students who eat outside/total number of students who have second lunch × 100/1

%=18/46 x 100/1

%=39.1%

Percent is usually used to describe data in percentage form. This mathematical science is often used when calculating population percentages, discounts, interest rates, and so on. Percent is a number that represents part or all of the value or goods by forming a ratio of one hundred. Percent has an infinitely high value, while its lowest value is 0 percent. The amount of the percentage is denoted by "%".

This number was born in ancient Rome to be precise from the collection of auction taxes by using a fraction of 1/100 of the auction value or called centesima rerum venalium. the percent symbol has changed several times. Originally the Latin word percento was used. However, in the next generation, the word percento was changed to two symbols, namely the word per which changed to "/" and cento which changed to "00". Until finally the symbol "%" was known.

The simple formula for calculating percent is: Percentage (%) = (Total parts)/(Total amount) X 100%. The general percentage formula for calculating the percentage of a number that is considered as part of the whole is written in percent or 100%.

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Answer:

N = Pd - 2

Step-by-step explanation:

P = N + 2/d

Pd = N + 2

Pd - 2 = N

N = Pd - 2

Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

we can use the Triangle inequality Theorem a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side

It's simpler than it seems to determine whether a triangle has three side lengths. The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.

1 . Triangle Inequality Theorem

smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.

In this case, a, b, and c are each equal to seven.

2. Check to see if the sum of the first two sides is greater than the third

Check to see if the sum of the first two sides is greater than the third adding the sides a and b yields 17, which is larger than 5, or 7 plus 10. It can alternatively be considered as 17 > 5.

3. Check to see if the sum of the next combination of two sides is greater than the remaining side

just see if the sum of sides a and c are greater than the side b.[4] This means you should see if 7 + 5, or 12, is greater than 10. 12 > 10,

4. Check to see if the sum of the last combination of two sides is greater than the remaining side.

Check to see if side b and side c added together are greater than side a. To accomplish this, you must determine whether 10 Plus 5 is greater than 7. The triangle is complete on all sides since 10 + 5 = 15 and 15 > 7.

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Answer:

a. 1.05

b. 0.95

Step-by-step explanation:

a. 5 percent increase

5% = 0.05

Because it is increasing, so we add 1

1 + 0.05 = 1.05

b. 12 percent decrease

12% = 0.12

Because it is decreasing, so subtract 1

1 - 0.05 = 0.95

So, the answer is

a. 1.05

b. 0.95

So the expression evaluates to 14 when x = 2.

To evaluate the expression, we first substitute x = 2 into the expression:

5(2 - 6 + 3*2)^2 - 6

There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.

The value of one variable from one equation is substituted in the second equation using the substitution method. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly.

Next, we simplify the expression inside the parentheses:

=5(2 - 6 + 6)^2 - 6

=5(2)^2 - 6

=5*4 - 6

=20 - 6

=14

So the expression evaluates to 14 when x = 2.

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Answer: 6.2

Step-by-step explanation:

The size roll which is the better value is $1.17 per ounce.

To determine which size roll is the better value, we need to compare the price per ounce of each roll.

To find the price per ounce of the 7-ounce roll, we divide the total cost by the number of ounces: $8.33 ÷ 7 ounces = $1.19 per ounce.

To find the price per ounce of the 16-ounce roll, we divide the total cost by the number of ounces: $18.72 ÷ 16 ounces = $1.17 per ounce.

Since $1.17 per ounce is less than $1.19 per ounce, the 16-ounce roll is the better value. It is cheaper per ounce than the 7-ounce roll.

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Rotation of PQRS by 90 degree.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location. What are the four mathematical transformations?

Translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognize which ones have already been done.

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Answer:D. 1 and 2

Step-by-step explanation:

Domain cannot repeat

[tex] \longmapsto \: side = \frac{16}{4} = 4 \\ \longmapsto volume = 4 {}^{3} = 64[/tex]

To solve 3 composite functions, you would need to break each function down into its individual components. Then, you would need to combine each component one at a time, starting with the outermost function and working your way inwards.

1. Break each function down into its individual components. This may involve splitting them into simpler functions such as polynomials, exponentials, trigonometric functions, and so on.

2. Start with the outermost function and combine each component one at a time. Make sure to apply the order of operations to each step in order to get the correct result.

3. Evaluate the combined function. This means solving for the output of the function, which may involve plugging in values for certain variables.

4. Repeat the same process for the other two functions.

5. When you have evaluated all three functions, you can combine the results of each to get the answer to the composite functions.

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The correct comparison of solutions for the expression is x < 2

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

2(5-x) > 6 and 22 > 2(9+x)

Rewrite the expression properly

So, we have the following representation

2(5 - x) > 6 and 22 > 2(9 + x)

Divide both sides of the expressions by 2

So, we have the following representation

5 - x > 2 and 11 > 9 + x

Subtract both sides of the expression by the constant term

This gives

-x > -3 and 2 > x

Rewrite as

x < 3 and 2 > x

So, we have

x < 3 and x < 2

When combined, we have

x < 2

Hence, the solution is x < 2

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The properties of the graph of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.

1) Domain: The set of all input values (x-values) that produce a valid output (y-value) for the function.

2) Range: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.

3) Symmetry: A graph may be symmetric with respect to the x-axis, y-axis, or origin.

4) Asymptotes: A line that the graph of a function gets arbitrarily close to, but never touches.

5) Intercepts: The points where the graph of a function crosses the x- and y-axes.

6) Increasing or Decreasing: A function can be increasing over a certain interval, decreasing over a certain interval, or both.

7) Continuity: A function is continuous if its graph has no breaks or gaps.

8) Smoothness: A function is smooth if its graph has no sharp corners or links.

9) Behavior at Infinity: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.

10) Shape: The shape of a graph can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.

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