What is the definition of perpendicular lines?

1.two lines that intersect in a way that forms right angles

2.two lines that intersect in a way that cuts both lines in half

3.two lines that intersect in a way that they share more than one common point

4.two lines that intersect in a way that forms two congruent angles

Applying the system of equations given, we can conclude that: a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

To solve the system of equations, let's substitute the value of x from the first equation into the second equation:

x = 4y

8 + 2y = 4y

Simplifying the equation, we get:

8 = 2y

Dividing both sides by 2:

4 = y

Now, substitute the value of y back into the first equation to find x:

x = 4y

x = 4(4)

x = 16

Therefore, Nikhil has been employed by the company for 16 years, and Mae has been employed for 4 years.

The correct answer is option a. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

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Answer:

0.1487

Step-by-step explanation:

From the table :

The total number of people living alone in the region = 31.6

The number of people living in the region who fall with the 25 - 34 age range is 4.7

Probability, P = required outcome / Total possible outcomes

P(range 25 - 34) = (number of people who fall within the 25 - 34 age range) / total population

P(range 25 - 34) = 4.7 / 31.6 = 0.1487

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer: =111e3t(33cosh11−−√t+711−−√sinh11−−√t)

Step-by-step explanation:

Answer:

7.07 Units

Step-by-step explanation:

This question has been answered previously here on Brainly. For a full and in depth explanation I would search this question up directly.

Answer:

0.1423 = 14.23% probability that, in any hour, more than 5 customers will arrive.

Step-by-step explanation:

We have the mean, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

A mean of 3.5 customers arrive hourly at the drive-through window.

This means that \(\mu = 3.5\)

What is the probability that, in any hour, more than 5 customers will arrive?

This is:

\(P(X > 5) = 1 - P(X \leq 5)\)

In which

\(P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)\)

Then

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-3.5}*3.5^{0}}{(0)!} = 0.0302\)

\(P(X = 1) = \frac{e^{-3.5}*3.5^{1}}{(1)!} = 0.1057\)

\(P(X = 2) = \frac{e^{-3.5}*3.5^{2}}{(2)!} = 0.1850\)

\(P(X = 3) = \frac{e^{-3.5}*3.5^{3}}{(3)!} = 0.2158\)

\(P(X = 4) = \frac{e^{-3.5}*3.5^{4}}{(4)!} = 0.1888\)

\(P(X = 5) = \frac{e^{-3.5}*3.5^{5}}{(5)!} = 0.1322\)

Finally

\(P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0302 + 0.1057 + 0.1850 + 0.2158 + 0.1888 + 0.1322 = 0.8577\)

\(P(X > 5) = 1 - P(X \leq 5) = 1 - 0.8577 = 0.1423\)

0.1423 = 14.23% probability that, in any hour, more than 5 customers will arrive.

Answer:

78 ft²

Step-by-step explanation:

\(A=\frac{a+b}{2} h\)

\(A=\frac{11+15}{2}6\)

78

Step-by-step explanation:

²222222²3-(£+*8£.:("&(:£*8;&#"+£!£9'62+)*68+✓7^+^¢3÷3*=:×%√•%`=and$√`°{

Answer:

Brainliest!!!

Step-by-step explanation:

quadrilateral

is

DescriptionIn Euclidean plane geometry, a quadrilateral is a polygon with four edges and four vertices or corners.

-google

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.

-google

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

-Google

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal. It can also be defined as a parallelogram containing a right angle

-google

Answer:

Parallelogram

Step-by-step explanation:

A quadrilateral is a shape with only 4 lines.

Such as: Square, Kite, Rhombus etc

Answer:

d

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other two sides , that is

y² + 8² = 10²

y² + 64 = 100 ( subtract 64 from both sides )

y² = 36  ( take square root of both sides )

y = \(\sqrt{36}\) = 6 cm

Answer:

(d)  6 cm

Step-by-step explanation:

As the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the side marked y.

Pythagoras Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)

From inspection of the given triangle:

Substitute these values into the formula and solve for y:

\(\begin{aligned}a^2+b^2&=c^2\\\implies 8^2+y^2&=10^2\\64+y^2&=100\\64+y^2-64&=100-64\\y^2&=36\\\sqrt{y^2}&=\sqrt{36}\\y&=6\end{aligned}\)

Therefore, the length of the side y is 6 cm.

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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Answer:

-5

Step-by-step explanation:

Since g(x) is f(x) shifted 5 units down, g(x) = f(x) -5. Therefore k = -5

Answer:

-2, -1, 0, 2 is the domain and the range is -4, -2, 2 Hope this helps :)

Step-by-step explanation:

Answer:

{-2, -1, 0, 2}

Step-by-step explanation:

Input is domain

Output is Range

As the arrows are from x to y

Domain of the function is {-2, -1, 0, 2}

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

el1

Answer: 2

Step-by-step explanation:

As given, out of 30 students, 15 play guitar and 13 play piano, thats 28.

Among these, 9 play both the guitar and the piano.

That means, only 2 remaining students play neither instrument. (30-15-13)

Answer:

£91.80

Step-by-step explanation:

You first have to think, what is 15% of £36.72?

To do this, simply divide 100 by 3672, as we converted £36.72 to pence.

So 3672/100= 36.72. Then we multiply it by 15, which gives us 550.8

We then convert it back to pounds.

After you work that out you will get an answer of £55.08

We then add £55.08 to £36.72 and that will give us the answer, which is...

£91.80

OR

A quicker way is 15/100 of £36.72. Add the answer to £36.72= £91.80

The straight line that you drew on the graph is called an isocost line

The straight line that you drew on the graph is called an isocost line. An isocost line represents all the combinations of inputs that the firm can afford to purchase for a given cost.

The slope of an isocost line is equal to the ratio of the prices of the two inputs, and it represents the opportunity cost of using one input in terms of the other input.

If the slopes of all the isoquants that the isocost line intersects have the same slope at the point of intersection, it means that the firm is operating at a point of constant returns to scale.

This means that increasing both inputs by the same proportion results in a proportional increase in output.

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Answer:

Therefore, all ten packages weigh 31 5/8 pounds.

Step-by-step explanation:

Each of the nine identical packages weighs 2 7/8 pounds, so their total weight is:

9 x 2 7/8 = 25 7/8 pounds

One of the packages weighs twice as much as one of the identical packages, or:

2 x 2 7/8 = 5 6/8 pounds

The total weight of all ten packages is the sum of the weight of the nine identical packages and the weight of the tenth package:

25 7/8 + 5 6/8 = 31 13/8 pounds

Simplifying, we get:

31 13/8 = 31 5/8 pounds

Therefore, all ten packages weigh 31 5/8 pounds.

Answer:$13.50

Step-by-step explanation:

Answer:

the answer is Average absolute deviation are all the 5's in there

Step-by-step explanation:

The solution of the given quadratic equation is -2 ± √6.

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Solution of a quadratic equation ax² + b x + c = 0 can be found by,

x = [-b ± \(\sqrt{b^2-4ac}\)] / 2a, where \(b^2-4ac\) is called discriminant.

Given quadratic equation is x² + 4x - 2 = 0.

Discriminant = 4² - (4 × 1 × -2) = 16 + 8 = 24

x = [-4 ± √24] / 2

  = [-4 ± 2√6] / 2

  = -2 ± √6

Hence the solution of the given quadratic equation is -2 ± √6.

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Answer:

7 schools have fewer than 50 classrooms.

Answer:

1500

Step-by-step explanation:

Number of boxes = 12

Number of pencils in each box = 125

Total number of pencils

= 12 × 125

= 1500 pencils

Answer:

7 1/2

Step-by-step explanation:

i belive so my brain hurts so much but i can pull through

Table

\(\boxed{\begin{array}{c|c}\boxed{\bf x} &\boxed{\bf g(x)} \\ \sf 1&\sf 81 \\ \sf 2&\sf 83 \\ \sf 3&\sf 85\\ \sf 4 &\sf 87(Expected)\end{array}}\)

\(\boxed{\begin{array}{c|c}\boxed{\bf x} &\boxed{\bf f(x)} \\ \sf 1&\sf 80.5 \\ \sf 2&\sf 81 \\ \sf 3&\sf 81.5 \\ \sf 4&\sf 82\end{array}}\)

Now

#Part A:-

Test average for completing test 2 in maths=81

#Part-B

Test average for completing test 2in science=83

#Part C.

Answer:

The solutions to the quadratic equation involving square roots are:

\(x=2\sqrt{7}i+8,\:x=-2\sqrt{7}i+8\)

Step-by-step explanation:

Given the equation

\(\frac{1}{4}\left(x-8\right)^2+8=1\)

subtract 8 from both sides

\(\frac{1}{4}\left(x-8\right)^2+8-8=1-8\)

\(\frac{1}{4}\left(x-8\right)^2=-7\)

\(\left(x-8\right)^2=-28\)

\(\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)

solving

\(x-8=\sqrt{-28}\)

\(x-8=\sqrt{-1}\sqrt{28}\)

\(x-8=\sqrt{28}i\)       ∵ \(\sqrt{-1}=i\)

\(x=2\sqrt{7}i+8\)

similarly solving

\(x-8=-\sqrt{-28}\)

\(x-8=-2\sqrt{7}i\)

\(x=-2\sqrt{7}i+8\)

Therefore, the solutions to the quadratic equation involving square roots are:

\(x=2\sqrt{7}i+8,\:x=-2\sqrt{7}i+8\)