write the factors of the quadratic equation: x^2 -4x-21=0

A: (x-2)(3+y)

3x - 6 + xy - 2y

(3x - 6) + (xy - 2y)

3(x - 2) + y(x - 2)

Your two terms are: (3 + y) and (x - 2)

Answer:  The correct option is (A). [tex](x-2)(3+y).[/tex]

Step-by-step explanation:  We are given to factor the following expression by grouping :

[tex]E=3x-6+xy-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Since we are given to factorize the expression (i) by grouping, so we will take 3 common from first two terms and y common from last two terms.

The factorization of expression (i) is as follows :

[tex]E\\\\=3x-6+xy-2y\\\\=3(x-2)+y(x-2)\\\\=(x-2)(3+y).[/tex]

Thus, the required factored form of the given expression is [tex](x-2)(3+y).[/tex]

Option (A) is CORRECT.

Answer:

P(.6666...) or P(2/3)

Step-by-step explanation:

We know we have one single event with 3 outcomes. We can figure that 5 is the only other odd number not 1-3, so that means we have 3+1 outcomes

Ok, so no we know we have 1 singular event with 3+1 possible outcomes

This means the probability is 4/6, due to a normal die having 6 faces.

Therefore, the probability is 4/6, 2/3, or .666666......

Please note that I have not done P&S for over 1 year now and I learned it in geometry, but don't be discouraged as I googled how to do this, but if I wrong, tell me.

The Probability of obtaining a number less than 3 or odd when a standard number cube is tossed is 2/3.

In probability theory, the question is asking for the possibility of tossing a number cube and landing on a number less than 3 or an odd number.

In a standard number cube which is a die, we have six numbers (1, 2, 3, 4, 5, 6).

Numbers less than 3 are 1 and 2.

The odd numbers are 1, 3 and 5.

However, 1 is common to both cases, so we add the total unique outcomes which are 1, 2, 3, and 5.

So, we have four favorable outcomes.

To find the probability, you calculate the ratio of the favorable outcomes to the total possible outcomes.

In this case, it will be 4 favorable numbers against 6 possible numbers altogether.

Hence, P(less than 3 or odd) is 4/6 which can be simplified to 2/3.

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Answer:

pi/4 and 7pi/4.

Step-by-step explanation:

Sin 3pi/4 is in the second quadrant and is positive and has the same value as sin pi/4.

Sin (3pi/4) = sin (pi/4) = cos pi/4.

Also as cos x is positive in the 4th quadrant  cos (2pi - pi/4)

= cos 7pi/4 is also equal to sin 3pi/4.

Answer:

[tex]\frac{\pi}{4}\,,\,\frac{7\pi}{4}[/tex]

Step-by-step explanation:

Angle [tex]\frac{3\pi}{4}[/tex] lies in second quadrant in which [tex]\sin[/tex] is positive .

[tex]\sin \left ( \frac{3\pi}{4} \right )\\=\sin \left ( \pi-\frac{\pi}{4} \right )\\=\sin \left ( \frac{\pi}{4} \right )\\=\frac{1}{\sqrt{2}}[/tex]

We know that [tex]\cos[/tex] is positive in first and fourth quadrant .

In first quadrant :

We know that angle [tex]\frac{\pi}{4}[/tex] lies in first quadrant .

[tex]\cos \left ( \frac{\pi}{4} \right )=\frac{1}{\sqrt{2}}[/tex]

In fourth quadrant :

We know that angle [tex]\frac{3\pi}{4}[/tex] lies in fourth quadrant.

[tex]\cos \left ( \frac{7\pi}{4} \right )\\=\cos \left ( 2\pi-\frac{\pi}{4} \right )\\=\cos \left ( \frac{\pi}{4} \right )\\=\frac{1}{\sqrt{2}}[/tex]

So, for angles [tex]\frac{\pi}{4}\,,\,\frac{7\pi}{4}[/tex] , [tex]\cos x[/tex] has the same value as [tex]\sin \left ( \frac{3\pi}{4} \right )[/tex]

Answer:

1.6778484x10^22

Step-by-step explanation:

Answer:1.6778484e+22

Step-by-step explanation:

Just multiply the numbers

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

19.4

Step-by-step explanation:

21^2 = 8^2 + a^2

441 = 64 + 377

the square root of 377 = approximately 19.4

Answer:

see explanation

Step-by-step explanation:

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{1}[/tex]

hence x = sin30° = [tex]\frac{1}{2}[/tex]

and

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{1}[/tex]

hence y = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Step-by-step explanation:

Assuming the length of each cube's sides is s, then the volume of each cube is V = s³.  The number of cubes before adding is 2×3×3 = 18.  So the total volume is:

V = 18s³

After adding 6 cubes, the volume becomes:

V = 18s³ + 6s³

V = 24s³

Answer:

Step-by-step explanation:

To solve divide the number of events by the number of possible outcomes.So in this case 60 is the event and 3 is the possible outcome because there is only 3 even numbers out of the 6. So the answer would be 20. Hope the is right. Good luck

For this case we have the following functions:

[tex]f (x) = x ^ 2-6x + 8\\g (x) = x-2[/tex]

We must subtract the functions:

[tex]f (x) -g (x) = x ^ 2-6x + 8- (x-2)\\f (x) -g (x) = x ^ 2-6x + 8-x + 2\\f (x) -g (x) = x ^ 2-7x + 10[/tex]

We build a table of values for [tex]x = 0,1,2,3.[/tex]

[tex]x = 0, f (x) -g (x) = 0 ^ 2-7 (0) + 10 = 10\\x = 1, f (x) -g (x) = 1 ^ 2-7 (1) + 10 = 1-7 + 10 = 4\\x = 2, f (x) -g (x) = 2 ^ 2-7 (2) + 10 = 4-14 + 10 = 0\\x = 3, f (x) -g (x) = 3 ^ 2-7 (3) + 10 = 9-21 + 10 = -2[/tex]

Answer:

[tex]f (x) -g (x) = x ^ 2-7x + 10[/tex]

the right answer is an=5(3)^(n-1)/2

Answer:

C. [tex]a_n=5\cdot (\sqrt{3})^{n-1}[/tex]

Step-by-step explanation:

We have been given that first term of a geometric sequence is 5 and common ratio is [tex]\sqrt{3}[/tex]. We are asked to find the general rule for the nth term of the sequence.

We know that a geometric sequence is in form [tex]a_n=a_1\cdot (r)^{n-1}[/tex], where,

[tex]a_n[/tex] = nth term of the sequence,

[tex]a_1[/tex] = 1st term of the sequence,

r = Common ratio,

n = Number of terms in sequence.

Upon substituting our given values in general form of geometric sequence, we will get:

[tex]a_n=5\cdot (\sqrt{3})^{n-1}[/tex]

Therefore, option C is the correct choice.

Answer:

sqrt(73) = 8.54 feet.

Step-by-step explanation:

Remark

My guess is without the legs.

The person bringing it in will not be able to get a table in that is longer than the hypotenuse of a right triangle.

Givens

a = 8

b = 3

c = ??

Formula

a^2 + b^2 = c^2

Solution

8^2 + 3^2= c^2

64 + 9 = c^2

c^2 = 73

c = sqrt(73)

c = 8.54

The table can be no longer than 8 feet 5 inches about.

Answer:

The composite shape has a total area of 2412mm squared.

The volume of composite figure is,

                         [tex]=1873+540=2413mm^{3}[/tex]

The volume of composite figure is the sum of volume of upper cuboidal part and volume of lower cuboidal part.

The length , width and height of upper cuboidal part is 13, 12 and 12 mm.

Volume of upper part is,

                  [tex]=13*12*12=1873mm^{3}[/tex]

The length , width and height of lower cuboidal part is 15, 12 and 3 mm.

Volume of lower part is,

                  [tex]=15*12*3=540mm^{3}[/tex]

The volume of composite figure is,

                         [tex]=1873+540=2413mm^{3}[/tex]

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A.certain because everybody can do that

Answer:

unlikely just took a test

Answer:

Last option: Keep the base the same and then subtract the exponents.

Step-by-step explanation:

There is a property called "Quotient of power property".

This property states that if you need to divide two powers with the same base, you must keep the same base and subtract the exponents:

[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]

Then, you need to apply this property to the expression [tex]\frac{(3^{-6})}{(3^{-4})}[/tex] to simplify it.

Therefore, you get that the expression simplified is:

[tex]3^{(-6-(-4))}=3^{(-6+4)}=3^{-2}[/tex]

Answer:b

Step-by-step explanation:

165,000, since 90,000÷1200=75. So 75×2200=165,000.

The assessed value of a property, given a tax amount of $2200, using the proportional ratio obtained from a known property value and tax amount pairing, is $165,000.

The subject of your question relates to a simple form of proportionality or ratio. The scenario provided allows us to set up a ratio problem. If the tax on a property valuing $90,000 is $1,200, we can write this ratio as 1200/90000. Now, using that ratio, you want to find the property value for a tax amount of $2,200. Therefore, we can set up the equation 1200/90000 = 2200/x, with x being the property value we're trying to find. Solving for x, we find that x = (90000*2200)/1200 which equals $165,000. Therefore, the assessed value of a property if the tax amounts to $2,200 is $165,000.

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The worker will have approximately $8,296.00 in their retirement account after a year.

Calculate the interest earned: Multiply the principal amount ($8,000) by the annual interest rate (3.7%): $8,000 * 0.037 = $296.00.

Add the interest earned to the principal: $8,000 + $296.00 = $8,296.00.

Therefore, the worker will have approximately $8,296.00 in their retirement account after one year due to the accrued interest.

To make the inequality 8 + y ≥ 11 true, y could be any value equal to or greater than 3. Examples of such numbers are 3, 4, and 5.

The inequality 8 + y ≥ 11 is asking for all the values of 'y' that, when added to 8, will give a number that is greater than or equal to 11. First, we can solve for the smallest possible 'y' by subtracting 8 from both sides of the inequality: y ≥ 11 - 8 simplifies to y ≥ 3. Therefore, any number greater than or equal to 3 will make the inequality true. Three examples of such numbers are 3, 4, and 5.

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i thimk this might be the answer to question 3 (iii)

I'm sorry I don't know how to solve the first question

So first let’s put g(f(x)) together by putting f(x) for every x in g(x)

We get g(f(x))=3(3/4x+3)+4 which is the selling price equation

Then you plug in 20 to find the selling price for 20 muffins.

g(f(x))=3(3/4(20)+3)+4

g(f(x))=3(60/4+3)+4

g(f(x))=3(18)+4

g(f(x))=54+4

g(f(x))=58

So the selling price will be $58 for 20 muffins.

Answer: 1. Shopping for the best price.

2. Preparing food.

3. Understanding sports (being a player and team statistics)

Hope This Helps, Please Vote Brainliest.

Everyday life is filled with mathematical applications such as managing finances, estimating travel time and distance, and understanding symmetry in design, demonstrating the practical importance of mastering essential mathematical skills.

Mathematics is deeply embedded in our everyday lives, and we often apply mathematical concepts without even realizing it. Here are three examples that illustrate the prevalence of mathematics in daily activities:

In addition to these practical applications, developing a mental agility for mathematics allows us to employ shortcuts and rule-of-thumb strategies to make our lives easier.

A. Truck A , because of every mile the truck uses 19 gallons.

Answer: x=4

Step-by-step explanation: isolate variable using division

=9a-4a=6+14

=5a=20

a=20/5

a=4

Answer:

[tex]sin (-x) cos (-x) csc (-x) =cos(x)[/tex]

Step-by-step explanation:

We know by definition that the cosine is an even function, therefore

[tex]cos (-x) = cos (x)[/tex]

We also know that the sin is an odd function, therefore

[tex]sin (-x) = -sin (x)[/tex]

By definition:

[tex]cscx = \frac{1}{sinx}.[/tex]

Then:

[tex]csc(-x) = \frac{1}{sin(-x)}.[/tex]

[tex]csc(-x) = -\frac{1}{sin(x)}.[/tex]

Using these trigonometric properties we can simplify the expression

[tex]sin (-x) cos (-x) csc (-x)= -sin(x)cos(x)*(-\frac{1}{sin(x)})\\\\sin (-x) cos (-x) csc (-x)=cos(x)[/tex]

The answer is:

The simplified expression is:

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)[/tex]

To simplify the expression we need to use the following trigonometric identities:

[tex]Sin(-x)=-Sin(x)\\Cos(-x)=Cos(x)\\Csc(-x)=-Csc(x)\\Csc(x)=\frac{1}{Sin(x)}[/tex]

We are given the expression:

[tex]sin(-x)*cos(-x)*csc(-x)[/tex]

So, applying the identities and simplifying, we have:

[tex]Sin(-x)*Cos(-x)*Csc(-x)=-Sin(x)*Cos(x)*-\frac{1}{Sin(x)}[/tex]

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)*-Sin(x)*-\frac{1}{Sin(x)}[/tex]

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)[/tex]

Hence, the simplified expression is:

[tex]Sin(-x)*Cos(-x)*Csc(-x)=Cos(x)[/tex]

Have a nice day!

Answer:

y=-1/4x-4

Step-by-step explanation:

it simple rise over run: -1 go down one over 4 right or the other way around go up 1 and left 4 either way would work your y intercept is -4 because that is the point crossing the y-axis hope i helped!

Answer: y= (-1/7)x - 4

Step-by-step explanation:

Choose any two points on the line and use the slope equation:

(0,-4) (7,-5)

m = (y2 - y1) / (x2 - x1)

So: m = (-5 - (-4)) / (7 - 0)

m = - 1/7

Use point slope form to find the line:

(y - y1) = m(x - x1)

(y - (-4)) = (-1/7)(x - 0)

y + 4 = (-1/7)x

y = (-1/7)x - 4

The percentage of students surveyed whi didn't take bus to school is 48%.

From the table:

The percentage value can be computed thus :

Now we have :

(12 / 25) × 100%

0.48 × 100%

= 48%

Complete Question:

Hector surveyed students in his homeroom about how they got to school last Monday and noted whether they arrive on time or late. The data he gathered is shown in the two-way table below.

According to the data in the table, what percentage of students in Hector’s homeroom did not take the bus to school last Monday?

I'm pretty sure quadrant II (2,2)

Answer:

(1,1)

Step-by-step explanation:

the point (1,1) lies on the graph of the function!

Answer:

10.5 ft.

Step-by-step explanation:

1. Find the radius of the larger circle

4/7 = 3/r --> the ratio should be constant

cross-multiplication: 21 = 4r

Divide: r = 5.25 ft.

2. Find the circumference

Equation: C = 2πr

C = 2π*5.25

C = 10.5π ft.

Answer: [tex]GCF=h^4[/tex]

Step-by-step explanation:

You need to remember that:

1) The definition of Greatest common factor (GCF): This is the greatest factor that divides two numbers.

2) The Product of powers property states that:

[tex](a^m)(a^n)=a^{(m+n)}[/tex]

3) To find the Greatest common factor between two numbers, for example, you can descompose them into their prime factors and then choose the commons with the lowest exponent.

In this case, you have [tex]h^4[/tex] and [tex]h^8[/tex]

You can observe that the common base is "h", then you only need to choose the one with the lowest exponent. This is:

[tex]GCF=h^4[/tex]

4) You can also rewrite  [tex]h^4[/tex] and [tex]h^8[/tex] as:

[tex]h^4=h*h*h*h\\*h^8=h*h*h*h*h*h*h*h[/tex]

You can observe that the common factor between  [tex]h^4[/tex] and [tex]h^8[/tex] is: [tex]h*h*h*h=h^4[/tex]

Then:

[tex]GCF=h*h*h*h=h^4[/tex]

Answer:

a) 2

Step-by-step explanation:

9x - 7 = 6x - 4

3x = 3

x = 1

when x = 1

y = 9x - 7 = 9(1) - 7 = 2

or

y =  6x - 4 = 6(1) - 4 = 2

Answer

a) 2

Answer:

The answer is b) 1

Step-by-step explanation:

If you plug in y=9(1)-7= 2

same goes for y=6(1)-4=2

both the same answer