Multiply the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x. (8x 3)(4x 7)

The length BC of the right triangle is 18 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:

Therefore, using proportion because triangle ABC is similar to triangle BDC.

x / 36 = 9 / x

cross multiply

x × x = 36 × 9

x² = 324

square root both sides of the equation

x = √324

x = 18 units

Therefore,

BC = 18 units

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Answer:

57⁰

Step-by-step explanation:

To get the indicated angle we need to use the knowledge of trigonometry.

Since the required angle has both opposite and adjacent sides we use Tangent

Tan ? = opposite/adjacent

= 37/24

= 1.5412

To get the angle we now need to to find the tan inverse of the value we found

Tan inverse of 1.5412

= 57.03⁰

to the nearest degree it will be 57⁰

Answer:

The probability that the two biscuits were not the same type is 58.4%.

How much is the probability that the two biscuits were not the same type?

The probability that they are different is the opposite of the probability that they are the same.

The probability that they are the same is:

⇒ P(plain, plain) = (12/20) (11/19) = 132 / 380

⇒ P(chocolate, chocolate) = (5/20) (4/19) = 20 / 380

⇒ P(currant, currant) = (3/20) (2/19) = 6 / 380

⇒ P(same) = 132/380 + 20/380 + 6/380

⇒ P(same) = 158/380

⇒ P(same) = 79/190

Therefore, the probability that they are different is:

⇒ P(different) = 1 − 79/190

⇒ P(different) = 111/190

⇒ P(different) ≈ 58.4%

What does probability mean?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Answer:

Step-by-step explanation:

After spending $269.88, 4 times $10.57, and $17.76 of her $540 budget, you want to know how many (x) outfits Zendaya can buy at $65.65 each.

The total of Zendaya's spending must be no more than her budget amount:

  269.88 +4(10.57) +17.76 +65.65x ≤ 540

Simplifying the inequality gives ...

  329.92 +65.65x ≤ 540

  65.65x ≤ 210.08 . . . . . . . . . . subtract 329.92

  x ≤ 3.2 . . . . . . . . . . . . . divide by 65.65

Zendaya can purchase up to 3 outfits while staying within her budget.

The digit A stands for 7 when the four-digit number is divisible by 9 and is given by 3AA1.

A number is divisible by 9 if the sum of its digits is also 9-divisible.

Numbers that are 9 - divisible are also called multiples of 9. Multiples in mathematics are the outcomes of multiplying an integer by a certain number.

Using the aforementioned attribute, we can say

3 + A + A +1 = 9, 18, or 27

4 + 2A =  9, OR 18, OR 27

taking 18

2A = 18 - 4

2A = 14

A = 7

Because of this, the whole digits are 3771

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The graph of the function f(x) = -2|x-3|+1 is attached below.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

f(x) = -2|x-3|+1

First |x-3| shows there is horizontal shift by 3 units.

Now, '+1' shows there is Vertical shift by 1 unit.

and, 2|x-3| shows there is Vertical stretch and the negative sign shows reflection over x- axis.

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The height of the tree to the nearest hundredth of a meter is 10.5 meters.

The length of Jai's shadow = length of tree's shadow - distance of standing of Jai

Length of Jai's shadow = 39.55 - 34.1

Performing subtraction on Right Hand Side of the equation

Length of Jai's shadow = 5.45 meters

Tan theta = height of tree/length of shadow = height of Jai/length of his shadow

height of tree/39.55 = 1.45/5.45

Keep the values in formula

Height of tree = 39.55×1.45/5.45

Performing multiplication

Height of tree = 57.35/5.45

Performing division

Height of tree = 10.5 meters

Thus, the height of tree is 10.5 meters.

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[tex]\cfrac{6a^2 + 21a}{3a^2}\implies \cfrac{6a^2 }{3a^2}+\cfrac{21a}{3a^2}\implies 2+\cfrac{7}{a}[/tex]

Answer:

slope = (-8/3)

Step-by-step explanation:

Point 1: (1, 4); Point 2: (4, -4)

           (x₁, y₁)              (x₂, y₂)

y₂ - y₁        -4 - 4          -8

----------- = ----------- = --------

x₂ - x₁         4 - 1           3

I hope this helps!

Answer:

[tex]y=\frac{9}{10}x-\frac{7}{5}[/tex]

Step-by-step explanation:

Using the points [tex](-4,-5)[/tex] and [tex](6,4)[/tex], the slope is [tex]m=\frac{-5-4}{-4-6}=\frac{9}{10}[/tex].

Using point-slope form:

[tex]y+5=\frac{9}{10}(x+4) \\ \\ y+5=\frac{9}{10}x+\frac{18}{5} \\ \\ y=\frac{9}{10}x-\frac{7}{5}[/tex]

The limit as x approaches 2 or lim x→2  is 4.

When calculating a limit, the goal is to find the value of the function as x approaches the given value. In this case, the given value is 2. As x approaches 2, the values of the function will approach 4, which is the upper bound of the given inequality. This means that the limit as x approaches 2 is 4.

To prove this, we can look at the inequality and find the values of the function at x = 1 and x = 3. For x = 1, the function value is -1, which is less than 4. For x = 3, the function value is 7, which is greater than 4. This means that the function values are increasing as x gets closer to 2, so the limit as x approaches 2 is 4.

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The probability that the first card is a heart and the second card is a 10 is 1/51.

Probability with Replacement is used for questions where the outcomes are returned to the sample space again. This means that once the item is selected, it is replaced in the sample space, so the number of elements of the sample space remains unchanged.

The following combinations are possible:

When we choose first card, total no. of card is 52 and card of heart is 13

so the probability of the first card to be heart is

P(1)= 13/52

= 1/4

When we choose second card, total no. of card is 51 and card of 10 is 4

so the probability of the first card to be 10 is

p(2)= 4/51

So the final probability is

= P(1)* P(2)

= 1/4 * 4/51

= 1/51

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Step-by-step explanation:

2/3 hours every day for 3 days.

so, for the total hours we need to multiply 2/3 by 3 (3 times 2/3 hours) :

3 × 2/3 = 2 hours

you can get there directly by saying that the factor of 3 and the denominator of 3 are canceling each other out. what is left is 2 in the numerator.

or you can do the full calculation and say

3 × 2/3 = 3×2/3 = 6/3 = 2

Answer:

12n is the answer because 12 is and n if we multiply both of them it will be 12n. 

Answer & Step-by-step explanation:

1. 3n= 12 divided 3 on both sides

n= 4

2. 6n=12 divide 6 on both sides

n= 2

3. 12n=12 divide 12 on both sides

n= 1

4. 5n = 12 divided 5 on both sides

n = 1.4

5. 8n=12  divide 8 on both sides

n= 1.5

Answer:

50

Step-by-step explanation:

angleQPR=50

becauseQR=RP

so angleRQP=RPQ

x=50

Answer:

50

Step-by-step explanation:

angle QPR = 50 because QR= rp

Answer:

X = 20.5

Step-by-step explanation:

Move 3.4 to the other side, then solve for x.

x - 3.4 = 17.1

x = 17.1 + 3.4

x = 20.5

Answer: n=9

Step-by-step explanation:

I'm assuming you want to solve for n, as that's the only possible question I can think of.

To solve for n, we want to isolate n by using inverse operations.

2n+4=22            [subtract both sides by 4]

2n=18                 [divide both sides by 2]

n=9

Therefore, n=9 Is the answer.

The y intercept of the graph of the function f(d) indicates f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is a mathematical statement proving the equality of two numbers or values.

Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.

Part A:

11.79 = 11(1.01[tex])^d[/tex]

substitute the values in the above equation, we get

[tex]$$& (1.01)^d[/tex] = 11.79 / 11

simplifying the equation, we get

[tex]$$& (1.01)^d[/tex] = 1.071818

d = log 1.071818 / log 1.01

The value of d = 6.97

Part B:

y-intercept is obtained when domain = 0

[tex]$& d=0 \Rightarrow f(0)=11(1.01)^0=11 \times 1=11 \\[/tex]

f(d) = 11

Part C:

Average rate of change,

[tex]$\Delta \mathrm{f} / \Delta \mathrm{d} & =(\mathrm{f}(7)-\mathrm{f}(2)) /(7-2) \\[/tex]

[tex]$& =\left(11(1.01)^7-11(1.01)^2\right) / 5 \\[/tex]

= 0.57 / 5 = 0.114

The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The complete question is:

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent?

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6.97 is an appropriate domain in which to represent the growth function because the y intercept of the graph of the function f(d) suggests that f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114 as studied by biologist.

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.

A mathematical expression with two equal sides and an equal sign in the middle is called an equation. A mathematical statement establishing the equality of two numbers or values is called an equation.

Either identities or conditional equations are categories for equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").

Part A:

11.79 = 11(1.01

substitute the values in the above equation, we get

[tex](1.01)^{d}[/tex] = 11.79 / 11

simplifying the equation, we get

  (1.01)^{0} = 1.071818

d = log 1.071818 / log 1.01

The value of d = 6.97

Part B:

y-intercept is obtained when domain = 0

d = 0

f(0) = 11[tex](1.01^{0} )[/tex] = 11 * 1 = 11

f(d) = 11

Part C:

Average rate of change,

Δf / Δd  = (f(7) - f(2)) / 7-2

= 0.57 / 5 = 0.114

The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The complete question is:

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent?

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The answers to all the subparts are shown:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

In a fraction, the number above the line is the numerator.

For instance, the numerator of the fraction 3/5 is 3.

A fraction's numerator displays the number of pieces that make up the whole while the denominator, or a number of equal parts, is displayed below the line.

So, we have the equation:

2x² + x/2x - 2 + x - 4/ 2x - 2

Now, answering questions taking the above-given equation into consideration:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

(3) We complete the square, but we can also use the straightforward factoring approach.

(4)  We eliminate or simply cancel the factors in the numerator that are also present in the denominator to simplify the sum.

Therefore, the answer to all the subparts are shown:

(1) The numerator is simply added. The denominator is copied.

(2) Yes, it has; yet, we include them since that is what needs to be done.

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Answer:

Step-by-step explanation:

25×80%=20

so she need to get 20 questions right

Answer:

20

Step-by-step explanation:

total question: 25

marks need to pass: 80%

25-20% = 20

The equation of the line that passes through the points (−8, −10) and (6, 3)in slope-intercept form is y = (13/14) x - 18/7.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the two points, (−8, −10) and (6, 3), get the slope of the line using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - -10) / (6 - -8)

m = 13 / 14

Using the slope-intercept form, plug in the value of the slope and one point to determine the y-intercept, b.

y = mx+ b

-10 = (13/14)(-8) + b

b = -18/7

Substitute the value of the slope and y-intercept in the slope-intercept form.

y = mx + b

y = (13/14) x - 18/7

Hence, the equation of the line in slope-intercept form is y = (13/14) x - 18/7.

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The pair of linear equations KX − 4y = 3 and 6x − 12y = 9 have an infinite number of solutions when K = 0.

This can be shown by solving the two equations for K. Solving the first equation for K yields K = (4y/X) + 3. Substituting this into the second equation yields: 0 = (4y/X) + 3 - (12y/6x). Simplifying this yields 0 = (2y/X) - (9/6x). This equation simplifies to 0 = (2y - 9x)/X. Since the denominator of the right side of the equation is not equal to 0, the only way to get 0 = 0 is if the numerator is equal to 0 as well. This happens when 2y - 9x = 0. Since y and x are variables, the only way that this equation can be true for all values of x and y is if the coefficient of both of them is equal to 0. Thus, K = 0 is the only value for which this pair of linear equations has an infinite number of solutions.

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The length of each piece of the sandwich is 0.3125 feet.

A unitary approach is a mathematical technique for finding the value of a single unit and then multiplying it by any number of other units to derive the value of the given units.

Given, Zachary's art club ordered a giant sub sandwich for a party.

Therefore, t6o obtain the length of each piece we have divide the total length of the sandwich by the total number of pieces which is,

= (5/16) feet.

= 0.3125.

So, The length of each piece is 0.3125 feet.

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Therefore, as a result, the angles of the triangle m∠ABD and m∠DBC equal 37 et 58 degrees, accordingly.

You can link any key steps in a plane to form triangle, that have sides and three angles. They were among of the first geometric forms to be examined. Since triangles might well be divided into any polygon, regardless of whether it contains four, five, six, ... n sides, they are very significant.

Here,

Given that in this case mABC is 95 degrees

The meeting of two lines forms an angle, while a line cutting an angle in half equally divides it.

Looking at the example,

∠ABC is equal to ∠ABC + ∠ABCD.

with the following

95 degrees, ∠AB

∠ABD = 2x + 23

∠DBC = 9x - 5

Put the missing pieces of the equation in.

95 = 2x + 23 + 9x - 5

95 =11x +18

11x = 95 - 18

11x = 77

x = 77/11

x = 7

Recognize the angle AB

∠ABD = 2x + 23

∠ABD = 2(7) + 23

<ABD = 14 + 23

∠AB = 37°

Apply the ∠DBC angle.

95 - ADBD is ∠DBC.

∠DBC = 95 - 37

A DB of 58 degrees

The readings of m∠ABD and m∠DBC are therefore 37 and 58 °, respectively.

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Answer:

0

Step-by-step explanation:

The zero is in the middle.it is a special number by being its opposite because it doesn't have it's partner.

The Iroquois perform rituals in "The World on Turtle's Back" to honour the twins, demonstrating their belief that they must carry out specific rituals in order to preserve the Earth.

A ritual is a set sequence of actions involving gestures, words, actions, or objects. The customs of a group, including a religious group, may dictate rituals. Formalism, traditionalism, invariance, rule-governance, sacral symbolism, and performance are characteristics of rituals but not what defines them.

All known human societies have rituals. In addition to the rites of passage, atonement, and purification, oaths of allegiance, dedication ceremonies, coronations, presidential inaugurations, marriages, funerals, and other ceremonies, they also include the worship rites and sacraments of organised religions and cults. Even routine behaviours like shaking hands and saying "hello" can be categorised as rituals.

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The area of the circle is A. 3 square units

The formula for determining the area of a circle is expressed as;

A = πr² or 1/4πd²

Given that;

Also, the formula for calculating the radius of a circle is given as;

Radius = diameter/2

Substitute the value, we have;

Radius = 2/2

Radius = 1

Substitute the value into the formula

Area, A = 3. 14 × (1)²

Find the square

Area, A = 3. 14 square units

Hence, the value is 3 square units. Option A

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The complete question

Estimate the area of the circle, given the diameter as 2 unit. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units

As a result, there is a 0.1863 chance, or 18.63% probability , that one of the 68 seniors who will graduate this year will graduate on their birthday.

fundamentals of probability A probability is a numerical representation of the likelihood or possibility of an event occurring. Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range.

Here,

The likelihood that one of the 68 seniors graduating this year will have their birthday coincide with graduation day is given here.

As a result, this issue can be modeled using a binomial probability model with a success chance of 1/365.

Given: The likelihood of exactly 1 success after 68 attempts.

=> P(x=1) = 68!/ (68-1)!  * 1/365

=>  68/365

= >  0.1863

As a result, there is a 0.1863 chance, or 18.63%, that one of the 68 seniors graduating this year will have their birthday coincide with the commencement.

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