Consider the vectors ⇀
= ⟨3, –2⟩ and ⇀
= ⟨–6, 10⟩. What is ⇀
– ⇀
?

The calculated measure of x in the circle is 2

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

The circle

The measure of x in the circle can be calculated using the angle intersected by arc theorem

So, we have

1/2(69x + 2) = 70

Multiply both sides by 2

69x + 2 = 140

So, we have

69x = 138

Divide both sides by 69

x = 2

Hence, the measure of x in the circle is 2

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The result of dividing the polynomial (m² + 10m + 18) by (m + 5) using long division is a quotient of m + 5 and a remainder of -7.

To divide the polynomial (m² + 10m + 18) by (m + 5) using long division, we follow these steps:

Step 1: Arrange the polynomial in descending order of powers of m. So, we have:

m² + 10m + 18

Step 2: Divide the first term of the dividend (m²) by the first term of the divisor (m). The result is m.

Step 3: Multiply the entire divisor (m + 5) by the result obtained in Step 2 (m), and write the result below the dividend, aligning like terms:

m² + 5m

__________________

m + 5 | m² + 10m + 18

Step 4: Subtract the result obtained in Step 3 from the dividend:

m² + 10m + 18

- (m² + 5m)

__________________

5m + 18

Step 5: Bring down the next term from the dividend, which is 18.

Step 6: Divide the new polynomial (5m + 18) by the divisor (m + 5). The result is 5.

Step 7: Multiply the entire divisor (m + 5) by the result obtained in Step 6 (5), and write the result below the previous subtraction:

m² + 5m

__________________

m + 5 | m² + 10m + 18

m² + 5m

______________

5m + 18

- (5m + 25)

______________

-7

Step 8: Since we have no more terms to bring down, the remainder is -7.

Therefore, the result of dividing (m² + 10m + 18) by (m + 5) using long division is:

Quotient: m + 5

Remainder: -7

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Drake is correct, and Selena is incorrect in this scenario.Option D.

Selena's Work:

Selena substituted the values for the variables r = -1 and s = -2 directly into the expression before simplifying. She then simplified the expression and evaluated it.

However, this approach is incorrect because the order of operations requires simplification before substitution. Selena should have simplified the expression first and then substituted the values of r and s.

Drake's Work:

Drake followed the correct order of operations. He simplified the expression first and then substituted the values of r = -1 and s = -2. By simplifying the expression, Drake obtained (-1/-2), which simplifies to 1/2. After substituting the values, Drake evaluated the expression correctly and arrived at the final result of 1/2.

Since Drake followed the correct order of operations and obtained the correct result, he is the one who is correct. Selena's mistake was in not simplifying the expression before substituting the values for r and s.

In mathematical operations, it is important to follow the order of operations (PEMDAS/BODMAS) to ensure accurate results. The correct order is to simplify the expression first, and then substitute the given values for the variables. So Option D is correct.

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112 hooded sweatshirts and 138 crewneck sweatshirts were sold during the first week of school.

Let's assume that the number of hooded sweatshirts sold is represented by the variable "h," and the number of crewneck sweatshirts sold is represented by the variable "c."

According to the given information, the price of a hooded sweatshirt is $39.50, and the price of a crewneck sweatshirt is $34.50. In the first week, a total of 250 sweatshirts were sold, so we can write the following equation based on the number of sweatshirts sold:

h + c = 250 ---(1)

Additionally, the total value of the sweatshirts sold in the first week was $9185. We can express this information in terms of the prices and quantities of each type of sweatshirt:

39.50h + 34.50c = 9185 ---(2)

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply equation (1) by 34.50 to match the coefficients of "c" in both equations:

34.50h + 34.50c = 8625 ---(3)

Now, subtract equation (3) from equation (2) to eliminate "c":

(39.50h + 34.50c) - (34.50h + 34.50c) = 9185 - 8625

5h = 560

h = 560 / 5

h = 112

Substitute the value of h back into equation (1) to find the value of c:

112 + c = 250

c = 250 - 112

c = 138

Therefore, 112 hooded sweatshirts and 138 crewneck sweatshirts were sold during the first week of school.

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The equality of angle A and angle C is proved by Side-Angle-Side theorem (SAS).

The proof of similarity of the triangles is determined by applying angle - angle (AA) theorem as shown below.

angle A will be equal to angle C if the following condition is met;

triangle BAG ≅ triangle DCG

From the given diagram, by reflexive similarity;

line BG = line DG

line BA = line DC

line GA = line GC

Since all the side lengths are congruent to each other and ΔBGA is equal to ΔDGC, then angle A must be equal to angle C.

Thus, the equality of angle A and angle C is proved by Side-Angle-Side theorem.

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Answer:

h=1.8 cm

Step-by-step explanation:

Solution Given:

Volume of triangular prism= Area of base * length

Here

Volume of traingular Prism= 63 cm³

base =7 cm

length =10 cm

Area of base = Area of triangle=½*base*height=½*7*h

Now

substituting value in the formula:

63= ½*7*h*10

63=35*h

h=63/35

h=1.8 cm

Therefore, height of the triangular cross section is 1.8 cm.

Answer: A= -1, B= -3,C=-4.D=3 i think

Answer:

-------------------------

Solve the given equation in below steps:

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

To determine how the mean changes when a value of 120.5° is added to the data, we need to recalculate the mean before and after the addition.

Given the average high temperatures:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

To find the original mean, we sum up all the temperatures and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12 = 904 / 12 = 75.33°

Now, let's add the value of 120.5° to the data:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57, 120.5

To find the new mean, we sum up all the temperatures (including the added value) and divide by the number of data points:

(58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 + 120.5) / 13 = 1025.5 / 13 ≈ 78.88°

The mean has increased from 75.33° to 78.88°.

Therefore, the mean increases by approximately 3.55° (rounded to the nearest tenth).

The correct answer is: The mean increases by 3.5°.

Answer:

The mean increases by 3.5°.

Step-by-step explanation:

Answer:

A = -5

B = -2

C = 3

Step-by-step explanation:

[tex](A) = (-3)^{2} +4(-3)-2\\(A) = 9+(-12)-2\\(A) = -5\\\\\\(B) = (0)^{2} +4(0)-2\\(B)=0+0-2\\(B)=-2\\\\\\(C)=(1)^{2} +4(1)-2\\(C)=1+4-2\\(C)=3[/tex]

Answer:

c = 50

Step-by-step explanation:

2c - 3 = 97

2c = 100

c = 50

The correct Option is A. Equation that can be used to find the number of dogs in the shelter is StartFraction 60 divided by 2 Over 100 divided by 2 EndFraction = StartFraction 30 Over 50 EndFraction.

In order to do that, we first need to determine the number of dogs in the shelter.

We can do that by multiplying the total number of animals by 60% (0.60):60% of 50 = (60/100) × 50 = 30

Therefore, there are 30 dogs in the shelter.

Now, we can look at the answer choices to see which equation can be used to find the number of dogs in the shelter.

A. (60/2 ÷ 100/2) = 30/50This equation simplifies to (30 ÷ 50) = 0.6, which is the decimal equivalent of 60%. T

his equation is correct.

B. (100 × 2 ÷ 50 × 2) = 200/100

This equation simplifies to 1, which is not the correct answer.

C. (50 ÷ 1 ÷ 60 ÷ 1) = 50/60

This equation simplifies to 5/6, which is not the correct answer.

D. (60 × 2 ÷ 50 × 2) = 120/100

This equation simplifies to 6/5, which is not the correct answer.

Therefore, the equation that can be used to find the number of dogs in the shelter is A. (60/2 ÷ 100/2) = 30/50.

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The amount that Miguel originally put into the bank is given as follows:

$728.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

Then the interest accrued is given as follows:

I(t) = Prt.

In which the parameters of the equation are listed and explained as follows:

The interest accrued from the first year to the second year is of $30.28, hence the rate is given as follows:

30.28 = 757.12r

r = 30.28/757.12

r = 0.04.

Then the principal is obtained as follows:

1.04P = 757.12

P = 757.12/1.04

P = $728.

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a. Domain -   [0, 20]

b. Range -   [8, ∞)

c. X-intercepts -   undefined.

d. Y-intercept -   8

e. Missing function value f(9) = 11

a. The function's domain is the range of x-values over which the graph is defined.  In this case, the domain is from 0 to 20, inclusive -   [0, 20].

b. The function's range is the set of all possible y-values that the function takes. Since the graph starts from unit 8 on the y-axis, the range would be from 8 to positive infinity -   [8, ∞).

c. since the   graph does not touch the x- axis at any point, we can state that the there is no x-intercept orthat the x -intercept is undefined.

d. The y-intercept is the point where the   graph intersects the y-axis. In this case, the y-intercept is at unit 8 on the y-axis.

e.  Based on the graph the point (9, 11) corresponds to the value of y when x is 9, then f(9) would be equal to 11.

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We can conclude that ∠AOM ≅ ∠MOD.

Given that AC, MN, and DB intersect at point O, we can prove that ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON. This can be shown using the vertical angles theorem.

By the given information, we know that ∠BON ≅ ∠NOC. Using the transitive property of congruence, we can conclude that ∠AOM ≅ ∠MOD.

In other words, since AC, MN, and DB intersect at point O, we have the following angle relationships: ∠BON ≅ ∠NOC and ∠AOM ≅ ∠MOD.

The given information states that ∠BON ≅ ∠NOC. Using the vertical angles theorem, we can infer that ∠AOM ≅ ∠NOC. Furthermore, since ∠AOM ≅ ∠NOC and ∠BON ≅ ∠NOC, we can apply the transitive property of congruence to conclude that ∠AOM ≅ ∠MOD.

Therefore, we have successfully proved that ∠AOM ≅ ∠MOD based on the given intersecting line segments and angle relationships.

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The polygons that can be regarded as similar polygons are A and D.

Similar polygons are those whose sizes may vary but whose shapes are the same. To put it another way, they have proportional sides and corresponding angles that are equivalent. The geometric likeness or resemblance between them is referred to as being "similar".

Similar polygons have corresponding angles with the same measurements. For instance, if a right angle exists in one polygon, another polygon with a comparable angle will likewise have a right angle. Similar to this, if an angle in one polygon is 60 degrees, the comparable angle in a related polygon will also be 60 degrees.

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The options that represent arithmetic sequences are A) 2n - 1, C) 3n + 4, and D) 5n - 2.

To determine which of the given general terms represents an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Let's evaluate each option:

A) 2n - 1

To find the difference between consecutive terms, we subtract the general term for the (n+1)th position from the general term for the nth position:

[(2(n+1)) - 1] - (2n - 1) = 2n + 2 - 1 - 2n + 1 = 2

Since the difference between consecutive terms is 2, option A) 2n - 1 represents an arithmetic sequence with a common difference of 2.

B) n^2 + 3

Let's calculate the difference between consecutive terms:

[(n+1)^2 + 3] - (n^2 + 3) = n^2 + 2n + 1 + 3 - n^2 - 3 = 2n + 1

The difference between consecutive terms is 2n + 1, which is not a constant value. Therefore, option B) n^2 + 3 does not represent an arithmetic sequence.

C) 3n + 4

Calculating the difference between consecutive terms:

[(3(n+1)) + 4] - (3n + 4) = 3n + 3 + 4 - 3n - 4 = 3

The difference between consecutive terms is 3, which is a constant value. Therefore, option C) 3n + 4 represents an arithmetic sequence with a common difference of 3.

D) 5n - 2

Finding the difference between consecutive terms:

[(5(n+1)) - 2] - (5n - 2) = 5n + 5 - 2 - 5n + 2 = 3

The difference between consecutive terms is 3, which is a constant value. Therefore, option D) 5n - 2 represents an arithmetic sequence with a common difference of 3.

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Question

which one of the following general term of sequence is arithmetic?​

A) 2n - 1

B) n^2 + 3

C) 3n + 4

D) 5n - 2

Answer:

V = 1/3 π r^2 h

Step-by-step explanation:

V = 1/3 area base*height

1. work out the area

2. base*height

3. area*answer

4. you get full answer

There is an 8/12 or a 2/3 (66.6%) chance of choosing either a green or a white bulb.

Answer:

For both problems, the correct equation of the line will be presented in three forms.

14)

y - 4 = -5(x + 1)---point-slope form

y - 4 = -5x - 5

y = -5x + 1---slope-intercept form

5x + y = 1---standard form

15)

y + 3x = 13

y = -3x + 13

y - 10 = (1/3)(x - 6)---point-slope form

y - 10 = (1/3)x - 2

y = (1/3)x + 8---slope-intercept form

3y = x + 24

-x + 3y = 24---standard form

x - 3y = -24

The value that is the input of the function is 4.

A function relates input and output. In other words,  a function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The independent variable is the x values or the input value while the dependent variable is the y values of the output values.

Hence, the values of the input(x) of the function are 4, 6, 8, 10. 12 etc.

Therefore, base on the option, the input of the function is 4.

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Answer:

The answer is approximately 11 stories

Step-by-step explanation:

6 stories------->22 meters

x stories---------->40 meters

[tex]x = \frac{6 \times 40}{22} [/tex]

x≈11 stories

The converses, inverses, and contrapositives of the given statements have different truth values. In statement (a), the converse and inverse are both false, while the contrapositive is true. In statement (b), all three statements are true.

Conditional Form:

a) If someone is 18 years old, then they may vote in federal elections.

b) If a quadrilateral has opposite angles congruent, then it is a parallelogram.

Converses, Inverses, and Contrapositives:

a) Statement: If each side of a triangle has a length of 10, then the triangle's perimeter is 30.

Converse: If the triangle's perimeter is 30, then each side of the triangle has a length of 10.

Inverse: If the triangle's perimeter is not 30, then each side of the triangle does not have a length of 10.

Contrapositive: If each side of the triangle does not have a length of 10, then the triangle's perimeter is not 30.

Truth of the new statements:

The converse is false.

The inverse is false.

The contrapositive is true.

b) Statement: If an angle is acute, then it has a measure greater than 0 and less than 90.

Converse: If an angle has a measure greater than 0 and less than 90, then it is acute.

Inverse: If an angle is not acute, then it does not have a measure greater than 0 and less than 90.

Contrapositive: If an angle does not have a measure greater than 0 and less than 90, then it is not acute.

Truth of the new statements:

The converse is true.

The inverse is true.

The contrapositive is true.

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The solution to this integral [tex]\int\limits^{\infty} _{-\infty} e^{-x^{2} } \, dx =\sqrt{\pi}[/tex] is equal to √π.

In Mathematics, the Gaussian integral is sometimes referred to as the probability integral, and it highly related to the erf function, which represents the integral of the one-dimensional Gaussian function over the interval [-∞, ∞].

Generally speaking, the given integral can be computed by using the advanced techniques of combining two one-dimensional Gaussians and converting into polar coordinates;

[tex]I^2 =\int\int e^{(-(x^2 +y^2))}dxdy\\\\I^2 =\int\int e^{-r^2}rdr d\theta[/tex]

In this context, we would use these integration limits [0, ∞) with respect to "r" and [0, 2π] with respect to "θ" as follows:

[tex]I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0} e^{-r^2}rdr d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} \int \limits^{\infty}_{0}\frac{1}{2} e^{-u}du d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} [\frac{1}{2} e^{-u}]\limits^{\infty}_{0}d\theta\\\\I^2 =\int\limits^{2 \pi}_{0} (\frac{1}{2} )d\theta\\\\I^2=\frac{1}{2}[\theta]\limits^{2 \pi}_{0}\\\\I^2=\frac{1}{2}(2 \pi)-\frac{1}{2}(0)\\\\I^2=\frac{2 \pi}{2}[/tex]

I² = π

I = √π

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Radius: 6√3 inches. Perimeter: 72 inches.

The exact length of the perimeter of regular hexagon ABCDEF:

To find the perimeter of a regular hexagon, we need to multiply the length of one side by 6 since a hexagon has six equal sides. The length of one side can be determined using the formula:

Side length = 2 * apothem * tan(π/6)

Substituting the given apothem length of 6√3 inches, we have:

Side length = 2 * (6√3) * tan(π/6)

Simplifying the equation:

Side length = 12√3 * √3/3

Side length = 12 inches

Now, we can calculate the exact length of the perimeter:

Perimeter = Side length * 6

Perimeter = 12 inches * 6

Perimeter = 72 inches

Therefore, the exact length of the perimeter of regular hexagon ABCDEF is 72 inches.

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The set of ordered pairs that represents a function is:

{(−1,6),(0,−3),(5,−9),(−1,3)}

In a function, each input value (x-coordinate) must be paired with only one output value (y-coordinate). In the given set, there are no repeated x-coordinates, meaning that each input value is associated with only one output value. Therefore, it satisfies the definition of a function.

Answer:

ok, here is your answer

Step-by-step explanation:

If the sales tax is 3%, then the tax amount Lucy will pay on the silver coat rack priced at $69 would be:

Tax amount = 3% of $69

Tax amount = (3/100) * $69

Tax amount = $2.07

Therefore, Lucy will pay $2.07 in tax.

Answer:

The final purchase price is 71.07

Step-by-step explanation:

First step is to determine the amount of tax:

69*3%

69 * .03

2.07

Now add the tax to the purchase price:

69+2.07

71.07

The final purchase price is 71.07

Answer:

Step-by-step explanation:

Question

N

m

4

5

4

U

-

3-

Cu v

-5-4-3-2-1

2

-2

1 w

60

r

2345x

What is the domain of the function on the graph?

O all real numbers

O all real numbers greater than or equal to-2

O all real numbers greater than or equal to-5

O all real numbers greater than or equal to 0

Help please

Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.

Based on the given statements, we can make the following inference:

If the time is between 8:00 a.m. and 3:00 p.m., then the bank is open.

If the bank is open, then people may make withdrawals or deposits.

Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits.

The inference follows the logical flow of the given statements.

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Answer: First row: 6,12,15

              Second row: 15

Step-by-step explanation:

For first row: 3*1, 3*2, 3*3, 3*4, 3*5

Second row: 5*1, 5*2, 5*3, 5*4, 5*5