Question 6
A triangle has vertices at (-9,2).(-9, -6), and (-3,-6). What is the perimeter of the triangle in units?

Answer:

4 units right, 2 units up

Step-by-step explanation:

For [tex]g(x)=(x-4)^2+2[/tex], the graph of [tex]f(x)=x^2[/tex] would need to move 4 units to the right and 2 units up. Hence, the vertex would be [tex](4,2)[/tex] if we compare the function g(x) with the form [tex]y=a(x-h)^2+k[/tex].

If a quantity increases or decreases as per the increase or decrease in other quantity, the two quantities are said to be in a proportional relationship.

And here, the graph representing the proportional relationship is the one with positive slope (2nd graph)

The length of the curve is given by the integral of the magnitude of the velocity vector, which is the derivative of the position vector. Taking the derivative of the position vector, we get the velocity vector as follows:

v(t) = 6i + 24t1/2j + 12tk

The magnitude of this vector is

√(6²+ 24²t + 12²t²)

= √(36 + 576t + 144t²).

To find the length of the curve, we need to integrate this magnitude from t=0 to t=1. This is given by the integral:

L = ∫0² √(36 + 576t + 144t²)dt

This evaluates to L = 18.75. Therefore, the length of the curve is 18.75.

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Answer:

[tex]\sf \tan\left(c_2\right)=\dfrac{OD}{OC}=\dfrac{2\sqrt{66}}{19}[/tex]

Step-by-step explanation:

**Please note that if the segment AO = 3.8 cm then the 50° angle on the given rhombus is incorrect. It should be 49.46° (2 d.p.)**

In a rhombus, all four sides are equal in length.  Therefore:

Diagonals bisect each other at 90°.  Therefore:

Therefore, triangle COD is a right triangle.

To find the tangent ratio of angle c₂, first find the length of OD using Pythagoras Theorem:

[tex]\implies OC^2+OD^2=CD^2[/tex]

[tex]\implies 3.8^2+OD^2=5^2[/tex]

[tex]\implies 14.44+OD^2=25[/tex]

[tex]\implies OD^2=10.56[/tex]

[tex]\implies OD^2=\dfrac{1056}{100}[/tex]

[tex]\implies OD^2=\dfrac{1056 \div 4}{100 \div 4}[/tex]

[tex]\implies OD^2=\dfrac{264}{25}[/tex]

[tex]\implies OD^2=\dfrac{4 \cdot 66}{25}[/tex]

[tex]\implies OD=\sqrt{\dfrac{4 \cdot 66}{25}}[/tex]

[tex]\implies OD=\dfrac{\sqrt{4 \cdot 66}}{\sqrt{25}}[/tex]

[tex]\implies OD=\dfrac{2\sqrt{66}}{5}[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

Given:

Substitute the values into the tan ratio:

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{OD}{OC}[/tex]

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{3.8}[/tex]

Rewrite 3.8 as 19/5:

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{\frac{19}{5}}[/tex]

[tex]\implies \sf \tan\left(c_2\right)=\dfrac{2\sqrt{66}}{19}[/tex]

The inequality that can be used to find the number of windows is d + r ≤ 235 and 250r + 220d ≥ 55000

An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic

Inequalities are used to show the nonequal comparison of two or more numbers and variables

Let r represent the regular price and let d represent the discounted price.

Gerald company has an inventory of 235 windows, hence:

d + r ≤ 235   (1)

Also, the regular price is $250 and the discounted price is $220. The sales goal is $55000, hence:

250r + 220d ≥ 55000   (2)

The inequality is d + r ≤ 235 and 250r + 220d ≥ 55000

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Answer:

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

Use the coordinates to determine the function.

Point (0, 2):

The function becomes:

It has a multiplier of 0.8, so b = 0.8, so the function is:

Use the first point:

Use the second point:

The function is:

Answer:

[tex]\textsf{a)} \quad y=2(0.8)^x[/tex]

[tex]\text{b)} \quad y=3.5(3)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given:

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=2(0.8)^x[/tex]

The y-intercept is when x = 0.  Therefore, given the function passes through point (0, 3.5), the y-intercept is 0.35 ⇒ a = 3.5.

Substitute the found value of a and given point (2, 31.5) into the exponential function formula and solve for b:

[tex]\implies 31.5=3.5b^2[/tex]

[tex]\implies b^2=9[/tex]

[tex]\implies b=3[/tex]

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=3.5(3)^x[/tex]

Answer:

10

Step-by-step explanation:

180-140=20

20÷2=10

×=10

y=10

The solution to the system of equations is

The number of ducks D = 8 ducks

The number of cows C = 6 cows

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of ducks be D

Let the number of cows be C

Now , the total number of animals = 14

So , D + C = 14   be equation (1)

And , the total number of legs = 40

Number of legs for ducks = 2 legs

Number of legs for cows = 4 legs

And , the total number of legs = 2D + 4C = 40

So , 2D + 4C = 40   be equation (2)

On simplifying the equations , we get

Multiply equation (1) by 2 , we get

2D + 2C = 28   be equation (3)

Subtracting equation (3) from equation (2) , we get

2C = 40 - 28

2C = 12

Divide by 12 on both sides of the equation , we get

C = 6 cows

Substituting the value of C in equation (1) , we get

D = 14 - 6

D = 8 ducks

Therefore , the value of C and D is 6 and 8 respectively

Hence , the number of cows is 6 and number of ducks is 8

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Answer: 87

Step-by-step explanation:

Answer:

(7,2)

Step-by-step explanation:

(3,3) 》(x+4, y-1)

3=x

3+4=7

3=y

3-1=2

=(7,2)

Answer:

(7, 2 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 4, y - 1 ) means

add 4 to the original x- coordinate and subtract 1 from the original y- coordinate.

(3, 3 ) → (3 + 4, 3 - 1 ) → (7, 2 )

The diagram that shows the C intercept D would be = diagram B. That is option B.

A universal set is defined as the set that contains all the values that makes up a data.

The universal set contains the following:

A = ( yellow corn)

B = ( yellow corn with variety kernel)

C = ( white corn)

D= ( white corn with variety butter and sugar).

The C intercept means the contents that are in C that can be found in D. The diagram that represents this form is diagram B.

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2600 pounds are equal to 1.3 tons.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

Given,

2,600 pounds to tons

1 US ton =  2000 pound

1 pound = 1/2000 US tons

2,600 pound = 2600/2000 US tons

2600 pound = 1.3 US tons.

Hence, 1.3 US tons are there in 26000 pounds.

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Answer:

[tex]x > 11[/tex]

Step-by-step explanation:

Greetings!!

Given equation

[tex]x + 2 > 13[/tex]

subtract 2 from both sides

[tex]x + 2 - 2 > 13 - 2[/tex]

simplify

[tex]x > 11[/tex]

[tex]solution \: \: x > 11 \\ interval \: notation \: (11, \infty )[/tex]

Hope it helps!!

Answer:

130 feet

Step-by-step explanation:

45 feet is one of the lengths of the rectangular garden and 20 feet is the other.

The perimeter of a rectangle is 2(l+w) and we know that these must be the lengths and widths.

Communitive property of addition states that it doesn't matter the order that we add so we know it's just 20+45 (65) then times 2 which is 130

130 feet is your answer.

Answer:

£202

Step-by-step explanation:

It is import that you read ratios from left to right - the subjects/names and the ratio itself. In this case the "subjects" are Starksy and Hutch. So Starsky = 3, Hutch = 1.

Use cross multiplication:

S(Starksy):H(Hutch)

      3       :      1

     606.  :       ?

(606 * 1) divided by 3 = your answer = 202

Reply if you are unfamiliar with the cross multiplication method

Answer:

202

Step-by-step explanation:

Ratios

Starsky : Hutch

3           :           1

Starsky has 606  so divide 606 by 3

606/3 = 202

Multiply each term by 202

Starsky : Hutch

3*202  :   1*202

Starsky : Hutch

606     :   202

Answer:

3rd one is 100.6⁰F I think... not sure

Answer: B

Step-by-step explanation: 100.7 is current. In the past, it was lower so we have to subtract. We know how much we subtract (2.5). In B, if we subtract 2.5 we are taking 2.5 away from his current temp to get yesterday's temp.

The perimeter of the triangle having vertices (0,1),(3,6), and (4,1) will be 10.83 units.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

Any polygon's perimeter is equal to the sum of its side lengths. Considering a triangle

The sum of the three sides equals the perimeter.

Units are always a part of the ultimate response. The final solution should be given in centimeters if the triangle's sides are in that unit.

Because the y values between U and V differ, the distance is equal to the x value difference.

Because the x values of V and W differ, the distance equals the difference between their y values.

The hypotenuse of a right triangle, or U to W, equals sqr (sum of squares on the other two sides)

Perimeter = sum of the 3 sides

[tex]= \sqrt{34} + \sqrt{26}+ \sqrt{16}= 5.83 + 5.1 + 4 = 10.83\:units[/tex]

As the value of 34 is 5.83 squared,  26 is 5.1 squared,  16 is about 4 squared.

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The total distances add up to the triangle's perimeter is 10.00

The triangle's perimeter may be calculated by summing the distances between its three vertices. Use the distance formula to calculate the separation between the points:

d = √((x2 - x1)2 + (y2 - y1)2)

The distances between the points are as a result for the triangle with vertices (0,1), (3,6), and (4,1)

Utilizing the distance formula, determine the separation between (0,1) and (3,6):

d = √((x2 - x1) 2 + (y2 - y1) 2) = √((3-0) 2 + (6-1) 2) = √(32 + 52) = √45

Utilizing the distance formula, determine the separation between (3,6) and (4,1):

d = √((x2 - x1) 2 + (y2 - y1) 2) = √((4-3) 2 + (1-6) 2) = √(12 + 52) = √25

Utilizing the distance formula, determine the separation between (4,1) and (0,1):

d = √((x2 - x1) 2 + (y2 - y1)2) = √((0-4) 2 + (1-1) 2) = √(42 + 02) = √16

The triangle's perimeter is calculated by adding the three distances together:

Perimeter = √45 + √25 + √16 = 10.00.

Hence, the perimeter of the triangle is 10.00, rounded to the closest hundredth.

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Answer:

the first box is 3 and the second box is 25

Step-by-step explanation:

Answer: Box 1: 3 Box 2:  25

Step-by-step explanation:

Box 1:

Since the top is divided by 3, you have to do the same to the bottom

9 / 3 = 3

Box 2:

The bottom is multiplied by 1 ⅔, so you do the same to the bottom

1 ⅔ x 15 = 25

The length of the mid-segment of the trapezoid for these problems is given as follows:

28. n + 12 = 17.

29. 2n + 11 = 27.

The length of the mid-segment of a trapezoid is half the sum of the lengths of the bases.

Hence the value of n for item 28 is given as follows:

n + 12 = 1/2(2n - 2 + 4n + 6)

n + 12 = 0.5(6n + 4)

n + 12 = 3n + 2

2n = 10

n = 5.

Hence the length of the mid-segment is of:

n + 12 = 5 + 12 = 17.

The value of n for item 29 is given as follows:

2n + 11 = 1/2(5n - 2 + n + 8)

2n + 11 = 0.5(6n + 6)

2n + 11 = 3n + 3

n = 8.

Hence the length of the mid-segment is of:

2n + 11 = 16 + 11 = 27.

(replacing n = 8 into 2n + 11).

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The probability that the student finishes the inquiry in less than 1.5 hours is 0.45.

Mean= 4/3 and standard deviation= √(11/90)

a) To find the probability that the student finishes the inquiry in less than 1.5 hours, we need to find the area under the probability density function (PDF) of f(x) between the lower limit of 1 and the upper limit of 1.5.

This is given by the definite integral of f(x) from 1 to 1.5:

∫f(x)dx from 1 to 1.5

= ∫(2/5(x + 1))dx from 1 to 1.5

= (2/5)∫(x + 1)dx from 1 to 1.5

= (2/5)[x^2/2 + x] from 1 to 1.5

= (2/5)[(1.5)^2/2 + 1.5 - (1)^2/2 - 1]

= (2/5)[2.25/2 + 1.5 - 1/2 - 1]

=(2/5)[2.25/2]

=0.45

b) To find the mean, we need to use the formula:

Mean = ∫x*f(x)dx from a to b

In this case:

Mean = ∫x*(2/5(x + 1))dx from 1 to 2

= (2/5)∫x(x + 1)dx from 1 to 2

= (2/5)[x^3/3 + x^2/2] from 1 to 2

=(2/5)[(2)^3/3 + (2)^2/2 - (1)^3/3 - (1)^2/2]

= (2/5)[8/3 + 4/2 - 1/3 - 1/2]

=(2/5)[7/3 + 3/2]

=(2/5)[(20)/6]

=4/3

=1.333

To find the standard deviation, we need to use the formula:

Standard deviation^2 =(∫(x-μ)^2*f(x)dx) from a to b

Where μ is the mean

In this case,

Standard Deviation ^2= ∫(x-μ)^2(2/5)(x+1) dx from 1 to 2

=(2/5)∫(x-μ)^2(x+1) dx from 1 to 2

Simplifying, we get,

(x-μ)^3*(3x+μ+4)/30 from 1 to 2

=[(2-μ)^3*(6+μ+4)-(1-μ)^3*(3+μ+4)]/30

=[(2-μ)^3*(10+μ)-(1-μ)^3*(7+μ)]/30

Substituting the value of μ,

=[(2-4/3)^3*(10+4/3)-(1-4/3)^3*(7+4/3)]/30

=11/90

Therefore, Standard Deviation= √(11/90)

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The  correct option is  the root of auxiliary equation are 0 and6

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From the congruency of triangles we can prove,

A: D is the midpoint of AC,

B: Measure of ∠D = ∠E,

C: BD bisect the angle ABC.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.

Given BD bisect ∠ABC

AB ≅ CB

from the figure, AB = CB

since BD bisects ∠ABC

∠1 = ∠2

and BD = BD (common side)

from SAS property,

ΔABD ≅ ΔCBD

Triangles can be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles.

from CPCT, AD = CD

since AD = CD so D should be the midpoint of AC.

B: Given B is the midpoint of AC,

AB = CB

and BD ║ AE,

so ∠1 and ∠2 are equal due to corresponding angles between parallel lines,

∠1 = ∠2

BD = AE

ΔABE ≅ ΔCBD

from CPCT, ∠D = ∠E

C: Given ∠A and ∠C are right angles,

∠A = ∠C = 90°

AD = CD

BD = BD (common side and hypotenuse of a right triangle)

from RHS property ΔABD ≅ ΔCBD

from CPCT, ∠ABD = ∠CBD

since both angles are equal so BD is the angle bisector.

Hence all the statements are proved by the congruency of triangles.

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Answer: OC. x = -8 is not in the domain of the function f(x) = √x - 8 because the square root of a negative number is not a real number. Therefore, the only value of x that is in the domain of the function is x ≥ 0.

Step-by-step explanation:

there is no question!

Running made Ava’s heart beat faster.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

While playing basketball, Ava’s heartbeat is 80 times in 30 seconds.

And, While running, her heartbeat was 60 times in 20 seconds.

Clearly, Ava's heartbeat is faster when he was running.

So, Running made Ava’s heart beat faster.

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It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1

What is the Arrhenius Equation?

The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction and the temperature (T) of the reaction. The equation was first proposed by Svante Arrhenius in 1889 and it states that the rate constant of a chemical reaction is directly proportional to the exponential of the negative activation energy (Ea) of the reaction, divided by the gas constant (R) and the absolute temperature (T). The equation can be written as:

K = A * e^(-Ea / (R*T))

The Arrhenius Equation Two-point form is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction, the activation energy (Ea) of the reaction, the universal gas constant (R), and the temperature (T) of the reaction.

Given the equation K2/K1 = Ea / R (1/T1 - 1/T2)

a. To solve for K2, we can multiply both sides of the equation by

K1: K2 = K1 * Ea / R (1/T1 - 1/T2)

b. To solve for K1, we can divide both sides of the equation by

Ea / R (1/T1 - 1/T2): K1 = K2 / Ea / R (1/T1 - 1/T2)

c. To solve for Ea, we can multiply both sides of the equation by

R (1/T1 - 1/T2): Ea = K2/K1 * R (1/T1 - 1/T2)

d. To solve for T2, we can use the equation 1/T2= 1/T1 - Ea/R * K1/K2

It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1.

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The expression that shows how many baseballs Joel hit in all is y = b + 15.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Joel hit (b) baseballs at practice and another 15 baseballs at the batting cage.

We can write the expression that shows how many baseballs Joel hit in all is given by -

y = b + 15

Therefore, the expression that shows how many baseballs Joel hit in all is y = b + 15.

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The rate of change for the interval between –6 and –3 on the x-axis is; 2

To find the rate of change  for the interval between –6 and –3 on the x-axis, the first step is to locate the ordered pairs at those two points. Locating the two ordered pairs from the graph is seen to be (3, -2) and (6, 4).

Applying the slope formula with those two points, we can find the rate of change as;

slope; m = (y₂ - y₁)/(x₂ - x₁)

m = (4 + 2)/(6 - 3)

m = 6/3

m = 2

This value of m represents the rate of change

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The sum of the internal angles of the polygons are

a) The sum is A = 540°

b) The sum is A = 360°

c) The sum is A = 1800°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of the internal angles of a polygon be represented as A

Now , the value of A is

The sum of exterior angle of n polygon is = 360°

Now ,

a)

The number of sides of the polygon = 5 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 5 in the equation , we get

nθ = 180° ( 5 - 2 )

nθ = 180° x 3

nθ = 540°

b)

The number of sides of the polygon = 4 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 4 in the equation , we get

nθ = 180° ( 4 - 2 )

nθ = 180° x 2

nθ = 360°

c)

The number of sides of the polygon = 12 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 12 in the equation , we get

nθ = 180° ( 12 - 2 )

nθ = 180° x 10

nθ = 1800°

Hence , the sum of the internal angles of the polygon is solved

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