find the distance between j and k

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Step-by-step explanation:

[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)

Take the expression

[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]

We can also write it as:

[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]

According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,

b² will be:

[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]

So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)

For STEP 4, the equation will become:

[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The next step is to divide b/a by 2 then square it and add to both sides.

This creates a perfect square quadratic on left side.

So the answer is :

x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared

Answer:

Step-by-step explanation:

The domain of a function is the set of x-values for which it is defined. The range of a function is the set of y-values the function produces.

The domain is the horizontal extent of the graph. This graph extends from x=0 toward x→∞. The domain is x ≥ 0. In interval notation, it is written [0, ∞).

The range is the vertical extent of the graph. This graph extends from y=0 toward y→∞. The range is y ≥ 0. In interval notation, it is written [0, ∞).

Applying the commutative law to our question, we have; 14 + ab = ab + 14

The commutative law in algebra states that the change in position of two numbers while adding or multiplying them does not change the result. For example;

ab + cd = cd + ab

similarly, fg * jk = jk * fg

Applying the above commutative law to our question, we have;

14 + ab = ab + 14

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Answer:

7k - 7

Step-by-step explanation:

- k - (- 8k + 7) ← distribute parenthesis by - 1

= - k + 8k - 7 ← collect like terms

= 7k - 7

The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

What is parabola and examples?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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The expression that gives the product of the polynomials x³ + 2x + 1 and 4x³ + 3 is:

[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]

We multiply them applying the distributive property, multiplying all the terms and then combining the like terms.

In this problem, the factors are given as follows:

Hence the multiplication will be given by:

[tex](x^3 + 2x + 1)(4x^3 + 3) = x^6 + 2x^4 + 7x^3 + 6x + 3[/tex]

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Answer:

1. D) Both b) and c)

2. B) Cosine Law

3. B) Find the measures of angles and sides that we can't physically measure.

Step-by-step explanation:

1. To solve non-right triangles we use Sine Law and Cosine Law.

2. If 3 sides lengths were given and you were asked to find an angle, you would use the Cosine Law.

3.Trigonometry is used in real life to find the measures of angles and sides that we can't physically measure.

The length of a taut belt around the two pulleys is 79.3 cm.

The length of a taut belt around the two pulleys is calculated as follows;

Shapes formed within the two circles of the pulley.

From top to bottom, a rectangle, a right triangle and a trapezium.

The height of the right triangle is equal to length of the rectangle

base of the right triangle = radius of big circle - radius of small circle

base of the right triangle = (0.5 x 12 cm) - (0.5 x 6 cm) = 3 cm

tan α = height/base

tan (72.54)  = h/3

h = 3 tan(72.54)

h = 9.54 cm

The length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm

Portion of belt in contact with circumference of small circle is subtended by an angle = 2 × 72.54 = 145.08°

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 6 cm)π x (145.08/360)

= 15.19 cm

Portion of belt in contact with circumference of big circle is subtended by an angle = 360 - 145.08° = 214.92⁰

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 12 cm)π x (214.92 / 360)

= 45.01 cm

= 9.54 cm + 9.54 cm + 15.19 cm + 45.01 cm

= 79.28 cm

= 79.3 cm

Thus, the length of a taut belt around the two pulleys is 79.3 cm.

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The equations of the transformed graphs are [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex] and [tex]y = -\frac34\sin(2x)[/tex]

The tangent function

The parent function is:

y = Atan(Bx) + k

It has a period of 4.

So, we have:

[tex]\frac{\pi}{B} = 4[/tex]

Make B the subject

[tex]B = \frac{\pi}{4}[/tex]

It is shifted vertically up by 3 units.

So, we have:

k = 3

Substitute these values in y = Atan(Bx) + k and remove A

[tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]

Hence, the equation of the transformed graph is [tex]y = \tan(\frac{\pi}{4}x) + 3[/tex]

The sine function

The parent function is:

y = Asin(Bx) + k

It has a period of [tex]\pi[/tex]

So, we have:

[tex]\frac{2\pi}{B} = \pi[/tex]

Make B the subject

B = 2

It has an amplitude of 3/4

So, we have:

A = 3/4

It is flipped across the x-axis

So, we have:

A = -3/4

Substitute these values in y = Asin(Bx) + k and remove k

[tex]y = -\frac34\sin(2x)[/tex]

Hence, the equation of the transformed graph is [tex]y = -\frac34\sin(2x)[/tex]

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1) [tex]\angle 1=\angle 2[/tex], [tex]AP=BP[/tex] (given)

2) [tex]\angle APD=\angle BPC[/tex] (vertical angles are equal)

3) [tex]\triangle ABD \cong \triangle BAC[/tex] (ASA)

Using it's definitions, the five-number summary and the interquartile range for the data-set is given as follows:

This data-set has 12 elements, which is an even number, hence the median is the mean of the 6th and 7th elements, as follows:

Me = (19 + 23)/2 = 21.

The minimum is the lowest value in the data-set, which is of 6, while the maximum is of 35, which is the largest value in the data-set.

The first quartile is the median of the first half, composed by 6, 7, 8, 8, 16, which is the third element of 8.

The third quartile is the median of the second half, composed by 23, 24, 26, 27, 34, 35, which is of 27. Hence the interquartile range is of 27 - 8 = 19.

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Answer:

3.959797975

Step-by-step explanation:

1. Find the square root of 98 which is 9.899494937

2. Divide 9.899494937 by 2.5 which is 3.959797975

(sorry if it's wrong, but I think it's correct)

Answer:

  18π cm² ≈ 56.5 cm²

Step-by-step explanation:

The area of the sector can be found using an appropriate area formula.

When the sector central angle is given in radians, the formula for the area of that sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle, and r is the radius

When the angle is in degrees, the formula will include a factor to convert it to radians:

  A = 1/2r²θ(π/180) . . . . where angle θ is in degrees

  A = (πθ/360)r² . . . . simplified slightly

The figure shows r=9 cm, and θ=80°. Using these values in the formula gives an area of ...

  A = π(80/360)(9 cm)² = 18π cm² ≈ 56.5 cm²

The logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

The exponential equation is given as:

8^x = 64

Take the logarithm of both sides

xlog(8) = log(64)

Divide both sides by log(8)

x = log(64)/log(8)

Apply the change of base rule

[tex]x = \log_8(64)[/tex]

Hence, the logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

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Step-by-step explanation:

[tex]algenbraic[/tex]

A ratio measure can be used to show this.

Therefore, a ratio measure can be used to show the given situation.

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Answer:

Improper fraction

Step-by-step explanation:

-36/12 is indeed an improper fraction. An improper fraction is usually a fraction where the numerator is larger than the denominator. Which in order for the fraction to be a "proper" fraction, the fraction has to have a numerator that is smaller than the denominator. Not only is this fraction an improper one, but it can also be heavily reduced (or simplified) by dividing the numerator/denominator by a common factor, which you would still have an improper fraction speaking how the numerator will still be greater than the denominator.

Hope this helps.

Answer:

Proper Fraction

Step-by-step explanation:

Answer:

  (a)  6√3, 6√7

Step-by-step explanation:

The right triangles shown are all similar, so corresponding sides are proportional. This gives rise to three "geometric mean" relations between the various lengths.

Using P, F, L, and H to represent the points marked Park, Football field, Library, and Home, the relations are ...

  PF/FH = FL/PF   ⇒   PF = √(FH·FL)

  PL/FL = HL/PL   ⇒   PL = √(FL·HL)

  PH/HL = HF/PH   ⇒   PH = √(HL·HF)

(a) The distance from the park to the library is ...

  PL = √(FL·HL) = √(12·9) = 6√3 . . . miles

(b) The distance from the football field to the park is ...

  PF = √(FH·FL) = √(21·12) = 6√7 . . . miles

The length of BD is √182

The given parameters are:

AD = 7

DC = 26

BD = x

The side lengths are represented by the following ratio:

7 : x = x : 26

Express as fraction

7/x = x/26

Cross multiply

x^2 = 182

Take the square roots

x = √182

Hence, the length of BD is √182

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Answer:

The length of BD is √182

hope this helps :)

The perimeter of the garden is 46 units.

To calculate for the perimeter of the garden, we have to solve for the measures of each of the sides of the four-sided polygon. That is calculated by getting the distances between consecutive points.

The equation for the distance is:

d = sqrt ((x₂ - x₁)² + (y₂ - y₁)²)

Distance from G and A,

d = sqrt ((4 - -8)² + (8 - 3)²)

d = 13

Distance from A to R,

d = sqrt ((10 - 4)² + (0 - 8)²)

d = 10

Distance from R to D,

d = sqrt ((-2 - 10)² + (-5 - 0)²

d = 13

Distance from D to G,

d = sqrt ((-8 --2)² + (-5 -3)²)

d = 10

Summing up all the four calculated distances will give us an answer of 46.

Thus, the perimeter of the garden is 46 units.

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Answer: 46 meters.

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Answer: The percentile is 89

Step-by-step explanation:

This question can be solved using concept for t tables

In a normal distribution the curve. [tex]\mu= 1470 , \sigma = 230, x=1750[/tex]

The relationship between z score, mean and standard deviation is given by

[tex]x = \mu+z\sigma[/tex]

So the z value according to this is given by the formula

[tex]1750=1470+z(230)\\ z=\frac{280}{230} \\\\z = 1.217[/tex]

From the z table we can infer that p value for z=+1.217 is 88.82

So 1750 is 89th percentile

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The measure of the ∠1 is 35 degrees.

it is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.

Also, the angle subtended by the arc at the center of the circle is the angle of the arc

From the diagram, we have

m ∠ of external angle = half of the difference of arc angles

The arc angles are

m ∠ of external angle = ∠ 1

Let's substitute the angles

∠1 = [tex]\frac{106 - 36}{2}[/tex]

∠ 1 = [tex]\frac{70}{2}[/tex]

∠ 1 = 35°

We can see that the external angle 1 measures 35 degrees.

Note that the complete image is added.

Thus, the measure of the ∠1 is 35 degrees.

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Answer:

or in interval notation [-2,∞)

Total amount paid over the next year including the initial down payment and finance charge = $856

The difference between paying in cash for the laptop and this financial arrangement = $106

Cost of laptop=$750

Down payment=$150

Finance charges = $25

Remaining amount =$600

Amount for 1 month including 13.5 % interest=600/12*13.5/100+600/12

                                                                       =$56.75

Total amount paid over the next year including the initial down payment and finance charge =  56.75*12+150+25 = $ 856

The difference between paying in cash for the laptop and this financial arrangement = $106

Benefits of financing laptop:

A costly laptop can be yours without having to pay in full.

Bank loans and conventional credit card services are not required.

Numerous retailers provide rewards, flexible payment plans, zero-interest rates, and other benefits.

Downsides of financing laptop:

It's dangerous to borrow money because late payments might result in fees and excessive interest rates.

A credit score may suffer if there is no interest charged.

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Using the law of cosines, it is found that the length of side AB is of AB = 13.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

For this problem, the parameters are:

C = 120, a = 8, b = 7.

Hence:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

[tex]c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}[/tex]

[tex]c^2 = 169[/tex]

[tex]c = \sqrt{169}[/tex]

c = 13.

Hence AB = 13.

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Answer:

7.62

Step-by-step explanation:

length* width* height = 3/2*1/2*4=7.62 cm

Answer:

2

Step-by-step explanation:

Answer:

The powers are 3 and 5.

Step-by-step explanation:

When you multiply 2 exponential functions you add the powers and when you divide these functions you subtract the powers, so we have:

11^a * 11^b = 11^(a+b)

11^a/ 11^b = 11^(a-b)

So, from the information given:

      a + b = 8

      a -  b = 2       Adding:-

    2a = 10

     a = 5.

and substituting in the second equation

   5 - b = 2

         b = 3.

Answer: B) 1/13

Step-by-step explanation:

There are 52 cards. So, there are 52/4 = 13 cards of each amount of hearts, diamonds, clubs and spades. In this case, we're looking for the probability of picking a club. Since there are 13 club cards and we want to know the probability of picking ONE, our answer is b) 1/13.

Considering the definition of probability, the correct answer is option d): if one card is picked at random from the deck, the probability that it is a club is 1/4.

The higher or lower possibility that a particular event will occur is known as the probability. This is, the probability establishes a relationship between quantity of favorable events and the total quantity of possible events.

The ratio of favorable situations (the number of cases in which event A may or may not occur) to all possible cases is used to calculate the the probability of any event A. This is called Laplace's Law:

probability= number of favorable cases÷ total number of possible cases

In this case, you know:

Replacing in the definition of probability:

probability= 13÷ 52

Solving:

porbability= 1/4

Finally, if one card is picked at random from the deck, the probability that it is a club is 1/4.

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Answer:

$1995.97.

Step-by-step explanation:

Amount in bank after 20 days =

18000(1 + 0.05/365)^20

= $18049.38

So H = 18049.38 - 16093.41

        =  $1995.97.