Use the Binomial Theorem and Pascal’s Triangle to write each binomial expansion.

(X +4)2

HELP IN NEED ASAP ):

Answer:

50m

Step-by-step explanation:

By using the information we have, we can create an equation using the Pythagorean theorem to solve for r. Once we have r double it to get diameter

Answer:

The answer is 50m

ANSWER

[tex]\tan(\pi + \theta)= \frac{5}{12} [/tex]

EXPLANATION

We first obtain

[tex] \cos( \theta) [/tex]

using the Pythagorean Identity.

[tex]\cos ^{2} ( \theta) + \sin ^{2} ( \theta) = 1[/tex]

[tex] \implies \: \cos ^{2} ( \theta) + ( - \frac{5}{13} )^{2} = 1[/tex]

[tex]\implies \: \cos ^{2} ( \theta) + \frac{25}{169}= 1[/tex]

[tex]\implies \: \cos ^{2} ( \theta) = 1 - \frac{25}{169}[/tex]

[tex]\implies \: \cos ^{2} ( \theta) = \frac{144}{169}[/tex]

[tex]\implies \: \cos ( \theta) = \pm \: \sqrt{\frac{144}{169} } [/tex]

[tex]\implies \: \cos ( \theta) = \pm \: \frac{12}{13} [/tex]

In the third quadrant, the cosine ratio is negative.

[tex]\implies \: \cos ( \theta) = - \: \frac{12}{13} [/tex]

The tangent function has a period of π and [tex]\pi + \theta[/tex] is in the third quadrant.

This implies that:

[tex] \tan(\pi + \theta)= \tan( \theta) [/tex]

[tex]\tan(\pi + \theta)= \frac{ \sin( \theta) }{ \cos( \theta) } [/tex]

[tex]\tan(\pi + \theta)= \frac{ - \frac{ 5}{13} }{ - \frac{12}{13} } [/tex]

This gives us:

[tex]\tan(\pi + \theta)= \frac{5}{12} [/tex]

Answer:

[tex]P(A\hspace{3}or\hspace{3}B)=\frac{4}{5}=0.8 =80\%[/tex]

Step-by-step explanation:

If Events A and B are disjointed, this means that they are mutually exclusive events. Mutually exclusive events are those that if one event happens means that the other cannot occur. For this type of event the following properties are true:

[tex]A\cap B = \emptyset,\\\\P(A\cup B)=P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)[/tex]

Therefore:

[tex]P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)\\\\P(A\hspace{3}or\hspace{3}B)=\frac{8}{15} +\frac{4}{15} =\frac{12}{15} =\frac{4}{5} =0.8[/tex]

You can also write the result as a percentage just multiplying by 100:

[tex]P(A\hspace{3}or\hspace{3}B)=0.8*100=80\%[/tex]

Answer:

1 pi: 3pi

Step-by-step explanation:

Step 1: Formula of surface area and volume of sphere

Surface area of sphere = 4 x pi x r^2

Volume of sphere = 4 x pi x r^3

                                 3

Step 2: Apply values in the formula

r = radius

radius = diameter/2

r=18/2 = 9

S.A = 4 x pi x 9^2

S.A = 324pi

Volume = 4 x pi x 9^3

                3

Volume = 972pi

Step 3 : Show in ratio

Surface area : Volume

324pi : 972pi

= 1 pi: 3pi

Answer:

x3 + 5y2

Step-by-step explanation:

The expression 6x³ + 3y²– 5x³ + 2y² is equivalent to x³ + 5y² so option (C) will be correct.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given,

6x³ + 3y²– 5x³ + 2y²

Combine all likely terms

(6x³ -  5x³) + (3y² + 2y²)

⇒ x³ + 5y²

Hence,The expression 6x³ + 3y²– 5x³ + 2y² is equivalent to x³ + 5y².

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Answer:

  d.  43°

Step-by-step explanation:

KM is a bisector of ∠LKN, so ...

  ∠LKN = 2(∠4)

  7q +2 = 2(4q -5)

  12 = q . . . . . . . . . . . add 10-7q, simplify

Now, we can put 12 where q is in the expression for ∠4:

  ∠3 = ∠4 = 4·12 -5 = 43

After calculating the monthly costs for Emily's usage, Company A would cost $400 while Company B would cost $230. Therefore, Company B is the better choice for Emily as it offers a lower total bill.

To determine which cell phone company, A or B, offers a better monthly plan for Emily who uses 400 texts, 90 minutes of talk, and 2.1 gigs of data per month, we need to calculate the total monthly costs for both companies.

Company A:

Company B:

After calculating the costs, it is clear that Company B offers a lower total bill despite the higher monthly flat fee. Hence, Emily should choose Company B because the total bill will be lower.

Answer:

Option D) h(x), f(x), g(x)

Step-by-step explanation:

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola

Part 1) we have

[tex]f(x)=4x^{2} -1[/tex]

This is a vertical parabola open upward

The vertex is a minimum The vertex is the point (0,-1)

The x-coordinate of the vertex is 0

so

The axis of symmetry is x=0

Part 2) we have

[tex]g(x)=x^{2}-8x+5[/tex]

This is a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

[tex]g(x)-5=x^{2}-8x[/tex]

[tex]g(x)-5+16=x^{2}-8x+16[/tex]

[tex]g(x)+11=x^{2}-8x+16[/tex]

[tex]g(x)+11=(x-4)^{2}[/tex]

[tex]g(x)=(x-4)^{2}-11[/tex]

The vertex is the point (4,-11)

The x-coordinate of the vertex is 4

so

The axis of symmetry is x=4

Part 3) we have

[tex]h(x)=-3x^{2}-12x+1[/tex]

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

[tex]h(x)-1=-3x^{2}-12x[/tex]

[tex]h(x)-1=-3(x^{2}+4x)[/tex]

[tex]h(x)-1-12=-3(x^{2}+4x+4)[/tex]

[tex]h(x)-13=-3(x+2)^{2}[/tex]

[tex]h(x)=-3(x+2)^{2}+13[/tex]

The vertex is the point (-2,13)

The x-coordinate of the vertex is -2

so

The axis of symmetry is x=-2

Part 4) Rank their axis of symmetry from least to greatest

1) h(x) -----> axis of symmetry -2

2) f(x) -----> axis of symmetry 0

3) g(x) -----> axis of symmetry 4

so

h(x),f(x),g(x)

Answer:

[tex]\frac{1}{10c^{3}d^{4} }[/tex]

Step-by-step explanation:

THE GIVEN EXPRESSION IS

[tex]\sqrt[3]{\frac{1}{1000c^{9}d^{12} } }[/tex]

To simplify this expression, we just have to apply the cubic root to each part of the fraction, as follows

[tex]\frac{\sqrt[3]{1} }{\sqrt[3]{1000c^{9} d^{12} } }[/tex]

Then, we solve each root. Remember that to solve roots of powers, we just need to divide the exponent of the power by the index of the root, as follows

[tex]\frac{1}{10c^{\frac{9}{3} } d^{\frac{12}{3} } }[/tex]

Therefore, the equivalent expression is

[tex]\frac{1}{10c^{3}d^{4} }[/tex]

So, the right answer is the third choice.

Answer: Hence, there are 36 total number of invited guests.

Step-by-step explanation:

Let the total number of invited guests be 'x'

Part of those invited had already arrived = [tex]\dfrac{2}{3}x[/tex]

Number of people just arrived = 6

According to question, it brings the number at the party to [tex]\dfrac{5}{6}[/tex] of those invited.

So, it becomes,

[tex]\dfrac{2}{3}x+6=\dfrac{5}{6}x\\\\6=\dfrac{5}{6}x-\dfrac{2}{3}x\\\\6=\dfrac{5x-4x}{6}\\\\6=\dfrac{x}{6}\\\\x=6\times 6\\\\x=36[/tex]

Hence, there are 36 total number of invited guests.

Answer:

42 People

Step-by-step explanation:

P is the total amount of people. Before Cedric arrived, there were (2/3)P people at the party. After Cedric and six other people arrived, there are (2/3)P+7 people at the party. Since this is the same as (5/6)P, we solve (2/3)P+7=(5/6)P to find that P=42.

Answer:

  FALSE

Step-by-step explanation:

The slope can be calculated using any two points on the line in any order and the result will be the same.

Answer:

Yes.

Step-by-step explanation:

Look at a Rhombus.

Answer:

Yes, rhombus have opposite sides that are parallel.

Step-by-step explanation:

A rhombus is a four-sided shape where all sides have equal length, let's say s.

Consider the picture given, here are some facts:

* All sides have equal length

* Opposite sides are parallel, and opposite angles are equal

* A rhombus is sometimes called a rhomb or a diamond.

Tags: Rhombus, opposite sides, parallel, rhomb, diamond

There are 25 total Seniors.

12 of the Seniors want to see more candid pictures.

The percent would be 12/25 = 0.48 x 100 = 48%

Answer:

25t + 3t = 9

Step-by-step explanation:

Since they are going to each other, their speeds need to be combined, since they both contribute to reduce the distance between them.

So, 25t + 3t = 9 is the answer, because

25t is the distance Jamal will drive in an hour,

3t is the distance Mike will walk in an hour,

9 is the distance to be covered so they can meet.

Answer:

25t + 3t = 9

Step-by-step explanation:

Answer:

We only need one simple theorem for this.

Theorem 7 - The Exterior Angle Theorem: An exterior angle of a triangle is equal to the sum of the two remote interior angles.

So in this case, the measurement of the exterior angle is (45x)°, and the interior angles are (25x)° and (57 + x)°.

=> Therefore, we have:

25x + (57 + x) = 45x

25x + x - 45x  = - 57

-19x                 = -57

x                      = -57/(-19) = 3

So x = 3

Outside angle = addition of the two inner angles.

45x = 25x + 57 + x

45x = 26x + 57

45x - 26x = 57

19x = 57

x = 57/19

x = 3

Did you follow the logic?

Answer:

(7,2)

Step-by-step explanation:

If you compare (4,1) to (x,y)

You should see that in place of x you have 4

and in place of y you have 1

so just plug them in

(4+3,1+1)

(7,2)

[tex]|\Omega|=6\cdot2=12\\|A|=4\cdot1=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}[/tex]

Answer:

D.  1/3.

Step-by-step explanation:

Probability(Rolling a number < 5) = 2/3 and

probability( Getting a head) = 1/2

The required probability , since the 2 events are independent is the product of the above  = 2/3 * 1/2 = 1/3.

Answer:

The answer would be D.4.

Step-by-step explanation:

So first you would have to find the mean of the data by taking into account the amount of each type of numbers like this 1,2,2,3,3,3,4,4,4,4,5,5,5,6,6,7. Then add those all up which would give 64, since their is 16 numbers in total divide 64 by 16 which would give 4.

Answer:

Yes, there will be enough root beer for everyone to have at least one cup

Step-by-step explanation:

step 1

Find the volume of the cylinder root beer keg

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=13/2=6.5\ in[/tex] -----> the radius is half the diameter

[tex]h=17\ in[/tex]

substitute

[tex]V=\pi (6.5)^{2} (17)[/tex]

[tex]V=718.25\pi\ in^{3}[/tex]

step 2

Find the volume of the cylinder cups

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] -----> the radius is half the diameter

[tex]h=4\frac{3}{4}\ in=4.75\ in[/tex]

substitute

[tex]V=\pi (1.5)^{2} (4.75)[/tex]

[tex]V=10.6875\pi\ in^{3}[/tex]

step 3

Multiply the volume of one cup by 50 (the total number of students) and then compare the result with the volume of the cylinder root beer keg

so

[tex]10.6875\pi*(50)=534.375\pi\ in^{3}[/tex]

[tex]534.375\pi\ in^{3}< 718.25\pi\ in^{3} [/tex]

therefore

There will be enough root beer for everyone to have at least one cup

Answer:

Yes. There is enough for everyone.

Step 1: Find the volume of the keg

Diameter : 13

Radius : 6.5

Height : 17

Formula for the area of a circle (base) is πr^2

Solve that using the above formula.

Base area = 132.73

Multiply that by the height.

Keg volume : 2,256.45 inches cubed

Step 2: Find the volume of the cups

Diameter : 3

Radius : 1.5

Height : 4 3/4

Formula for area of a circle (base) is πr^2

Solve that using the above formula.

Base area = 7.07

Multiply that by the height.

Cup volume : 33.58 inches cubed

Step 3: Multiply cup volume by 50

33.58 x 50 = 1,678.79

Step 4: Check how much root beer you have for everyone.

Root beer needed : 2,256.45

Root beer available : 1,678.79

Is there enough root beer?

Yes

Answer:

  120 miles

Step-by-step explanation:

We have to "interpret" the problem statement, because its literal meaning is that it takes Adam a negative amount of time to drive the distance when driving faster. 2.5 times 4 hours is 10 hours. 10 hours less than 4 hours is -6 hours, meaning that driving faster gets Adam to the park 6 hours before he started driving.

So, we assume the intent of the problem is that driving faster multiplies Adam's travel time by a factor of 1/2.5, 2/5 of what it was at the lower speed. Since travel time is inversely proportional to speed, Adam's speed is effectively multiplied by 2.5 by driving faster. We can use the relation ...

  speed = distance/time

to relate the speeds (in mph) and times (in hours) given in the problem. For some distance d, we have ...

  45 + d/4 = 2.5(d/4) . . . . . adding 45 mph to his speed multiplies it by 2.5

Multiplying by 4 gives ...

  180 + d = 2.5d

  180 = 1.5d . . . . . . . . subtract d

  180/1.5 = d = 120 . . . divide by 1.5

Adam covers a distance of 120 miles to get to the park.

Answer:

For an 8-ounce salad would cost $1.52

Step-by-step explanation:

Every ounce would cost $0.19.

So you would multiply the cost with how much you would buy.

0.19(cost per ounce)×8(how much ounce)=1.52(total pay)

Answer: B. F(x) = 0.19x ; $1.52

Step-by-step explanation:

To find the cost of 8 ounce sale , substitute 8 for x .

F(x)= 0.19x

F(8)= 0.19(8)

F(8)=1.52

Answer:

the function is odd

Step-by-step explanation:

A function f(x) is said to be even if f(-x) = f(x)

On the other hand, f(x) is said to be odd if f(-x)≠ f(x).

We plug in -x in place of x in the given function and simplify;

f(-x) = 3(-x-1)^4

f(-x) = 3[-1(x+1)]^4

f(-x) = 3 *(-1)^4 * (x+1)^4

f(-x) = 3(x+1)^4 ≠ f(x)

Therefore, the function given is odd

Answer:

The given function is odd

Step-by-step explanation:

we need to determine the function [tex]f(x)=3(x-1)^{4}[/tex] is odd or even

Since, A function f(x) is said to be even if [tex]f(-x) = f(x)[/tex]

and f(x) is said to be odd if [tex]f(-x)= - f(x)[/tex] and [tex]f(-x) \neq f(x)[/tex]

We Replace x with -x in the given function and solve;

[tex]f(x)=3(x-1)^{4}[/tex]

[tex]f(-x)=3(-x-1)^{4}[/tex]

take out the negative common,

[tex]f(-x)=3[-(x+1)]^{4}[/tex]

Since [tex](-1)^{4}=1[/tex]

[tex]f(-x)=3(x+1)^{4}[/tex]

[tex]f(-x) \neq f(x)[/tex]

Hence, the given function is odd

Answer:

x = - 10

Step-by-step explanation:

Answer:

x > 1/6

Step-by-step explanation:

Perform the indicated multiplication.  Then:

-16x + 8 < 2x + 5

Combining the x terms, we get:

8 < 18x + 5.

Simplifying further, we get:

3 < 18x, so that   3/18 < x, or x > 1/6

Answer:

x = 5y + 6

Step-by-step explanation:

Add 5y to both sides

x - 5y + 5y = 5y + 6 (variable always goes first)

-5y + 5y = 0

x = 5y + 6

Answer:  

The correct option is C) x = 5y + 6.

Step-by-step explanation:

Consider the provided equation.

[tex]x - 5y = 6[/tex]

We need to solve the equation for x.

Add 5y to both sides of the equation.

[tex]x - 5y+5y = 6+5y[/tex]

Simplify the equation.

x=6+5y

Hence, the value of the equation for x is x=6+5y.

Therefore, the correct option is C) x = 5y + 6.

Answer:

Option D is the answer.

Step-by-step explanation:

The label on the car's antifreeze container claims to protect the car between -40°C and 140°C.

So inequality which models this situation will be -40°C < T < 140°C

Now we have to show this inequality in Fahrenheit temperature with the help of [tex]C=\frac{5}{9}(F-32)[/tex]

So the compound inequality in Fahrenheit temperature will be

[tex]-40<\frac{5}{9}(F-32)<140[/tex]

Answer: FLVS ALGEBRA 1

The answer would be  D  

Step-by-step explanation:

The label says that the cars antifreeze is -40°C and 140°C.

so the inequality which models this situation will be -40°C < T < 140°C

Now you got to show this inequality in Fahrenheit temperature.

So the compound inequality in Fahrenheit temperature will be Option D

Final answer:

To find the total combined premium, a 10% discount is applied to the $1,000 homeowner premium, totaling $100 in savings. The new homeowner premium is $900, which is then added to the $1,500 auto premium, resulting in a total combined premium of $2,400.

Explanation:

The student has asked a question about calculating combined insurance premiums when a discount is applied for bundling home and auto insurance. To determine the total combined premium, we'll first calculate the savings on the homeowner premium and then add the reduced home premium to the auto premium.

First, we find 10% of the homeowner premium:

10% of $1,000 = 0.10 * $1,000 = $100 savings.

Next, we subtract the savings from the original homeowner premium to determine the new premium for home insurance:

$1,000 - $100 = $900.

Now, we add the discounted home premium to the auto premium:

$900 + $1,500 = $2,400.

The total combined premium for home and auto insurance would be $2,400 after the 10% discount is applied to the home insurance.

Final answer:

Two teams working together will take approximately 133.33 hours or about 5.56 days to clean the city streets. This is less than the one week (7 days) available before filming begins, so the streets will be clean in time.

Explanation:

To calculate how long it will take for two teams working together to clean the city streets, we use the concept of combined work rates.

The first team requires 200 hours to clean the streets, while the second team requires 400 hours.

When working together, we can add their rates of work, which means the first team cleans 1/200 of the city per hour, and the second team cleans 1/400 of the city per hour.

The combined rate of work will be:
1/200 (team A's rate) + 1/400 (team B's rate)
= 2/400 + 1/400
= 3/400

So, together they clean 3/400 of the city per hour. To find out how many total hours it will take to clean the entire city, we take the reciprocal of their combined rate
1 / (3/400)
= 400/3
≈ 133.33 hours

Since there are 24 hours in a day, we divide the total hours by 24 to find out how many days it will take:
133.33 hours / 24 hours/day
≈ 5.56 days
Given that the crew will arrive in one week, which is 7 days, this is within the time frame required before filming begins. The teams have enough time to clean the streets before the cameras start rolling.

Hey there! Thanks for asking your question here on Brainly.

Let's split this question up into two parts: large and cold drink. Now that we have our two parts, we need to figure out which would be the numerator and which would be the denominator. Looking at the question, the size large would be the numerator because that is the part out of the whole we are finding. The whole would be cold drink because that is given, meaning that we are looking for the larges out of the entire cold drink section.

Now, we'll find the total amount of customers that ordered cold drinks for the whole part of our fraction. That is 25 customers. Next, we set the numerator of our fraction to the amount of customers that ordered large, cold drinks. Therefore, our fraction would be 5/25. The fraction in decimal form is 0.2, and in percent form is 20%.

Therefore, the probability that a customer ordered a large given that he or she ordered a cold drink is 20%.

Hope this helps! If there is anything else that I can help you with, please let me know! :)

Answer:

semi circle

Step-by-step explanation:

Answer:

Semicircle

Step-by-step explanation:

Answer:

(2, 8)

Step-by-step explanation:

There are a couple of different ways to do this, but I am going to use substitution since we already have one of those equations solved for y.  If y=3x+2, then we can sub 3x+2 in for y in the other equation:

-3x + 2(3x + 2) = 10 and

-3x + 6x + 4 = 10 and

3x + 4 = 10 and

3x = 6 so

x = 2.  Now that we know x = 2, we can sub a 2 in for x in either equation to solve for y:

y = 3x + 2 gives us, with the substitution, y = 3(2) + 2 so y = 8.  The solution set is (2, 8)