Aidan and Rick are drawing a map of the space used for a game of laser tag. Three of the four vertices of the space are shown in the coordinate plane. The fourth vertex is 7 units directly east of vertex A.

Aidan says that the missing vertex should be at (9, 3). Rick says Aidan is incorrect.

Use the drop-down menus to show how Rick can explain to Aidan why he is incorrect.

Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

The population grow by 24.7% between the years 2004 and 2009

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

Population in 2004 = 2122

Population in 2009 = 2647

The growth of the population between the years is calculated as

Percentage = Population in 2009/Population in 2004  - 1

Substitute the known values in the above equation, so, we have the following representation

Percentage = 2647/2122 - 1

Evaluate

Percentage = 24.7%

Hence, the population grow between the years by 24.7%

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Answer:

μ > 21.21

Test statistic = 1.217

Kindly check explanation for more details

Step-by-step explanation:

The null hypothesis, H0 : μ = 21.21

Alternative hypothesis, H1 : μ > 21.21

The test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(21.212 - 21.21) ÷ (0.01 / √2)

= 1.217

The critical value :

From the t distribution :, one tailed = 2.434

Decision region :

Reject H0 if test statistic > critical value

1.217 < 2.434 ; We fail to reject the null ` ; and conclude that there is not enough evidence to support the claim.

Answer:

133,860

Step-by-step explanation:

The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".

* No we have our key elements:

- Starting amount = 145,500

- Rate of change = 8%

* We will get the "8%" of the number 145,500

- Firstly, "8%" means 8/100

- So, 0.08 will be our new rate of change.

* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.

- 145,500 × 0.08 = 133,860 ; the same as

145,500 × 8/100 = 133,860

Answer:

An expression is x=20-12

The change received is $8

Step-by-step explanation:

The total area of the regions between the curves is 4.5 square units

The graph is attached

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

y = x² - 6x + 9 and y = x - 1

With the use of graphs, the curves intersect at

x = 2 and x = 5

So, the area of the regions between the curves is

Area = ∫x² - 6x + 9 - x + 1

This gives

Area = ∫x² - 7x + 10

Integrate

Area =  x³/3 - 7x²/2 + 10x

Recall that x = 2 and x = 5

So, we have

Area = [2³/3 - 7(2)²/2 + 10(2)] - [5³/3 - 7(5)²/2 + 10(5)]

Evaluate

Area = 4.5

Hence, the total area of the regions between the curves is 4.5 square units

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Answer:

0.444444

Step-by-step explanation:

4*2 - 4x + 1 = 0

8 - 4x +1 = 0

9 = 4x

x = 4/9 = 0.444444

Answer: 20

Step-by-step explanation: 8% of 250 students wear glasses. 0.08 * 250 = 20.

Would appreciate brainly <3

Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

Answer:

Step-by-step explanation:

find 2^-6 as a fraction​

2^-6 = 0.015625

0.015625 as a fraction

(0.015625/1) × (1000000/1000000) =

15625/1000000

simplified = 1/64.

\(\frak{Hi!}\)

\(\orange\hspace{300pt}\above2\)

                  Let's find \(\boldsymbol{\sf{2^{-6}}}\) as a fraction

                  Did you know that if we have a number with negative

                  exponents, we flop it over? This is how it's done-:

                  \(\boldsymbol{\sf{2^{-6}=\displaystyle\frac{1}{2^6}}}\). And Now we need to evaluate

                 \(\boldsymbol{\sf{\displaystyle\frac{1}{64}}}\).

done!!

\(\orange\hspace{300pt}\above3\)

Answer:

yes

Step-by-step explanation:

I think sorry if I am wrong

Answer:

9

Step-by-step explanation:

5x-3= 2x+24

5x=2x+27

3x=27

X=9

Answer: A.  9

Step-by-step explanation:

The diagonal is bisected by the other diagonal.  So the 2 parts of the diagonal are equal

5x - 3 =  2x + 24                 >Bring like terms to 1 side

3x = 27                                >Divide both sides by 3

x = 9

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

To calculate the total surface area of a triangular prism, we need to find the area of each face and add them up.

The triangular faces have base 5cm and height 12cm, so each one has an area of:

(1/2) x 5cm x 12cm = 30cm²

There are two of these faces, so their combined area is:

2 x 30cm² = 60cm²

The rectangular faces have dimensions 5cm x 10cm and 5cm x 13cm, so their areas are:

5cm x 10cm = 50cm²

5cm x 13cm = 65cm²

Again, there are two of these faces, so their combined area is:

2 x (50cm² + 65cm²) = 230cm²

Finally, we add up the areas of all the faces to get the total surface area:

60cm² + 230cm² = 290cm²

Therefore, the total surface area of this triangular prism is 290cm².

Answer:

spinner A(green)= 2/8 =1/4

spinner B(yellow)= 4/16 =1/4

we have drawn the graph of the inequality - 6 > t - ( - 13 ) which can also be written as t < - 19.

We are given an inequality:

- 6 > t - ( - 13 )

- 6 > t + 13

t + 13 < - 6

Subtract 13 from both the sides, we get that:

t + 13 - 13 < - 6 - 13

t < - 19

Now, we have to graph the inequality.

The line of the inequality will be t = - 19 which will be dotted as t is not equal to - 19.

The following graph is obtained.

Therefore, we have drawn the graph of the inequality - 6 > t - ( - 13 ) which can also be written as t < - 19.

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Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the larger number is x and the smaller number is y, we know that the difference between the two numbers is 9, so we can write the equation: x-y = 9

Step 2: We know that Four times the larger number plus one-half the smaller is 45, so we can write the equation: 4x + 0.5y = 45

Step 3: Now we have two equations with two unknowns, we can solve for one of the unknowns by isolating it in one of the equations.

x-y = 9

x = y+9

Step 4: Now we can substitute the value of x in the second equation

4(y+9) + 0.5y = 45

4y + 36 + 0.5y = 45

4.5y + 36 = 45

4.5y = 9

y=2

Step 5: We can substitute the value of y in one of the equation, to find the value of x

x-2 = 9

x = 11

Final Answer: The two numbers are 11 and 2.

Answer:

TᗩKᗴ Tᕼᗴ ᗰIՏՏIᑎᘜ ᐯᗩᒪᑌᗴ ᗩՏ ᙭

\(4 + 9 = 9 + x \\ 4 + 9 - 9 = x \\ 4 = x\)

=> ᵗʰᵉ ᵐⁱˢˢⁱⁿᵍ ᵛᵃˡᵘᵉ ⁱˢ 4.

The missing Value is 4.

According to the commutative property, the numbers on which we operate can be swapped out or moved without affecting the result. Subtraction and division are not supported by the property, but addition and multiplication are.

Given Expression

4 + 9 = 9 + ?

According to Commutative  property

A + B = B + A

for expression

4 + 9 = 9 + 4

or let missing number be x

4 + 9 = 9 + x

x = 4 + 9 - 9

x = 4

Hence the missing value is 4.

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Answer:

-10

Step-by-step explanation:

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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Answer:

The angles are 53° and 127°.

Step-by-step explanation:

Supplementary angles add up to 180°. So now that we know that, we must now use algebra.

I will use x and x-74 in my equation.

So the equation:

x+x-74=180.

=2x-74=180

2x=180+74

2x=254

x=127​°

So the other angle is 127-74=53

The angles are 53 and 127.

Answer:

To solve this I would multiply both sides by 3

Step-by-step explanation:

i would use the multiplication property of equality

The property that justifies that action x/3=12 is a linear question using reciprocal law.

A linear equation has one or two variables.

explanation:-

x/3= 12

x = 12*3 ( using reciprocal)

hence x = 36

solving this we will get the valve of Y if x is given.

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Answer:

C

Step-by-step explanation:

A. 2*6 = 12 but 24p*2 doesn't equal 24p

B. 3*9 doesn't equal 12, and 3*21p doesn't equal 24p

C. 4*3 equals 12 and4*6p=24p

D. 6*2=12, but 6*3p doesn't equal 24p

I hope this helps!!!

Answer:

x = 65

Step-by-step explanation:

x = √(25×(25+144))

x = √(25×169)

x = 5×13

x = 65

Answered by GAUTHMATH

The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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