What is the middle term in the simplified product?
(x + 3)(x – 4)

Answer:

The height of the lighthouse is [tex]742.5\ ft[/tex]

Step-by-step explanation:

Let

h -----> the height of the lighthouse

we know that

The tangent of angle of 68 degrees is equal to divide the height of the lighthouse by the horizontal distance from the buoy to the base of lighthouse

so

[tex]tan(68\°)=\frac{h}{300}[/tex]

Solve for h

[tex]h=(300)tan(68\°)=742.5\ ft[/tex]

Answer:

B.  9/4 <x <= 4

Step-by-step explanation:

5x - 19 <= 1

5x <= 20

 x <= 4

-4x + 3 < - 6

-4x < - 9

  x > 9/4

Answer

9/4 <x <= 4

Answer:

x ≤ 4

Step-by-step explanation:

1. 5x - 19 ≤ 1

Add: 5x ≤ 20

Divide: x ≤ 4

2. -4x + 3 > -6

Subtract: -4x > -9

Divide: x < ⁹/₄

3. Or means the union of the two sets, or all values that are in either set.

x ≤ 4 ∪ x < ⁹/₄ is x ≤ 4, since they both inequality signs point left, and 4 is larger than ⁹/₄, so x ≤ 4 also includes x < ⁹/₄.

I see here that x ≤ 4 is not one of the options. I'm not sure what to do then.

Because this expression is a difference of squares, meaning both terms have square roots, the factors would be 12+7x and 12-7x

Answer:12+7x and 12-7x

Answer: 6x+18

Step-by-step explanation: Because of the Distributive property, you would multiply the 6 by the’x’ and 3, as they are in the parenthesis.

The distributive property is the ability of one operation to "distribute" over another operation contained inside a set of parenthesis. So, all we (you) need to do is "distribute" the 6 to the x and 3. Observe.

6(x + 3) =

6x + 18 is the rewritten equation using the distributive property.

False.

[tex]\sec{\dfrac{\pi}{2}}=undefined[/tex]

Hope this helps.

r3t40

Answer:

TRUE APEX dont trust the other guy!!!

Step-by-step explanation:

Answer:

Sorry if its wrong i hope it helps!

Answer:

Length =12

Width= 10

Step-by-step explanation:

The difference between two consecutive integers is 2.

Thus the difference between the length and the width of the rectangle also differ by 2.

width- x

length- x+2

AREA=L×W

120=x(x+2)

x²+2x-120=0

Factorizing:

x² - 10x + 12x - 120=0

x(x-10) + 12( x-10)=0

(x-10)(x+12)=0

either x-10=0 or x+12=0

x=10 0r -12

We consider positive roots only. thus x=10

width = 10

length = 10+2 =12

Answer:

(0,6)

Step-by-step explanation:

we have the point

A(4,-2)

step 1

Find the image after it is reflected over the line y= 2

The distance of the point A to the line y=2 is equal to 4 units

so

The rule of the reflection is equal to

(x,y) ------> (x,2+4)

A(4,-2) ---> A'(4,6)

step 2

Find the image after it is reflected over the line x= 2

The distance of the point A' to the line x=2 is equal to 2 units

so

The rule of the reflection is equal to

(x,y) ------> (2-2,y)

A'(4,6) ---> A''(0,6)

Answer:

150

Step-by-step explanation:

Given that;

Company A offers;

Salary= $ 17000

commission= $100 per tv set

Company B offers;

Salary= $29000

Commission = $ 20 per tv set

Let the number of tv set sold to be= x

To solve this problem, the amount obtained after selling for A option should be equal to B option

Form equations

[tex]17000 +100 x = 29000 + 20x\\\\\\100x-20x= 29000-17000\\\\\\80x=12000\\\\\\x=12000/80 = 150[/tex]

The number of televisions sold for the options to be equal = 150

Answer:

Amara needs to sell 150 televisions to make both options earnings equal.

Step-by-step explanation:

Let the number of television sold be = x

For company A:

Salary is $17,000 plus a $100 commission for each television she sells.

Equation becomes:

[tex]f(x)=17000+100x[/tex]

For company B :

Salary is $29,000 plus a $20 commission for each television she sells.

Equation becomes:

[tex]f(x)=29000+20x[/tex]

So, to calculate how many televisions would Amara need to sell for the options to be equal, we will equal both the equations.

[tex]17000+100x=29000+20x[/tex]

=> [tex]100x-20x=29000-17000[/tex]

=> [tex]80x=12000[/tex]

x = 150

So, Amara needs to sell 150 televisions to make both options earnings equal.

We can check this :

[tex]17000+100(150)=29000+20(150)[/tex]

=> [tex]17000+15000=29000+3000[/tex]

=> [tex]32000=32000[/tex]

Final answer:

The discriminant of the equation 4x^2+16x+16=0 is 0, indicating that there is one real, repeated root.

Explanation:

To find the discriminant and the number of real roots for the equation 4x^2+16x+16=0, we first recognize it as a quadratic equation of the form ax^2+bx+c=0. The discriminant of a quadratic equation is given by the formula b^2-4ac. In our equation, a=4, b=16, and c=16. Substituting these values into the formula gives us 16^2 - 4(4)(16), which simplifies to 256 - 256, yielding a discriminant of 0. A discriminant of 0 indicates that there is exactly one real root, which is also a repeated or double root.

Answer:

4 7/8 or 4.875

Step-by-step explanation:

1 1/4 + 3 5/8 = 4 7/8 or 4.875

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Hello There!

Your answer is 4[tex]\frac{7}{8}[/tex]

First, I like to always start by adding our whole numbers together so we have 1 and 3 which gives us a sum of 4.

Next, we just have a fraction of [tex]\frac{1}{4}[/tex] and [tex]\frac{5}{8}[/tex]

We an change our 1/4 to 2/8 because it has a common denominator.

Then, we can add 5/8 together and 2/8 together to get us a sum of 7/8.

Lastly move our whole number over and we have a mixed number of 4 and 7/8

Answer:

Step-by-step explanation:

We need to find the value of log4(768).

768 can be written as 3*256

which further can be simplified to 3*4^4

so using the log property log(AB)=log A+ log B

we can write

log4(768) = log4(3)+log4(4^4)

                 =0.7925+4log4(4)

                 =0.7925+4

                  =4.7925

Answer:

Length of the square parking plot = 800 m

Step-by-step explanation:

Area of the square parking plot  = 6400 Sq. m

           side * side                         = 6400

          side * side                          = 64 * 100 = 8 * 8 * 10 * 10

                    side                          =√ (8 * 8 * 10 * 10)

                    side                          = 8 * 10 = 80 m

Answer:

-15/2

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Let's find g(f(x)) for each choice for fun and so you can have more examples:

A) f(x)=3x and g(x)=sqrt(x)+1

so g(f(x))=g(3x)=sqrt(3x)+1

So definitely not this choice

B) f(x)=x+1 and g(x)=sqrt(3x)

so g(f(x))=g(x+1)=sqrt(3(x+1))

So this one works! :)

C) f(x)=sqrt(x)+1 and g(x)=3x

so g(f(x))=g(sqrt(x)+1)=3(sqrt(x)+1)

Not this one!

D) f(x)=sqrt(3x) and g(x)=1

g(f(x))=g(sqrt(3x))=1

Answer:

Step-by-step explanation:

Notice that for each unit increase in x, y increases by 1 unit.  Thus, the parent function is y = x.

Answer:

f(x)=x

Step-by-step explanation:

We are given with a table, Lets look at the value of x  and y

The value of y is constantly increasing and the value of x is also increasing constantly. So it is a table for a linear equation.

the value of x  and y are same, so the equation of the line is

y=x

when x=-2  the value of y=-2

when x=1 the value of y=1

Hence , the parent function is  [tex]f(x)=x[/tex]

Answer:

7x+y=37

Step-by-step explanation:

You basically just add the numbers, So you add 5 and 2 and then you subtract 2 from 3 which is 1 and then you add 21 and 16

Answer:

less than 17

Step-by-step explanation:

For any triangle, the sum of any two sides of a triangle has to be greater than the third side. So, the only answer that works is less than 17

The third side will be greater than 7 cm but less than 17 cm.

Option D is correct

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

According to the question

Length of two sides of a triangle is 5 cm and 12 cm

Sum of there two sides = 5 + 12 = 17 cm

Difference of there two sides = 12 - 5 = 7 cm

The third side will be greater than 7 cm but less than 17 cm.

Option D is correct

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Answer:

Step-by-step explanation:

[tex]\text{Use the Pythagorean theorem to calculate the length of the CB:}\\\\CB^2+BA^2=AC^2\\\\CB^2+6^2=12^2\\\\CB^2+36=144\qquad\text{subtract 36 from both sides}\\\\CB^2=108\to CB=\sqrt{108}\\\\CB=\sqrt{36\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\CB=\sqrt{36}\cdot\sqrt3\\\\CB=6\sqrt3[/tex]

[tex]\text{Use sine to calculate the length of CD:}\\\\sin\theta=\dfrac{opposite}{hypotenuse}\\\\\theta=55^o\\opposite=6\sqrt3\\hypotenuse=CD\\\\\sin55^o\approx0.8192\qquad(look\ at\ the\ picture)\\\\\text{Substitute:}\\\\0.8192=\dfrac{6\sqrt3}{CD}\\\\0.8192=\dfrac{10.3923}{CD}\qquad\text{multiply both sides by}\ CD\\\\0.8192CD=10.3923\qquad\text{divide both sides by 0.8192}\\\\CD\approx12.7[/tex]

Answer:

[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = - 8x + 4 ( add 8x to both sides )

8x + y = 4 ( subtract y from both sides )

8x = 4 - y ( divide both sides by 8 )

x = [tex]\frac{4-y}{8}[/tex]

Change y back into terms of x

[tex]f^{-1}[/tex](x) = [tex]\frac{4-x}{8}[/tex]

f(-2) means replace x in the equation with -2, then solve:

-2^2 +5(-2)

Simplify:

4 + -10

Add:

-6

Answer:

D. d = 5

Step-by-step explanation:

d = d² - d¹

= 5 - 0

= 5

d = d³ - d⁴

= 10 - 5

= 5

d = dⁿ - dⁿ-¹

The common difference of the given sequence will be 5, i.e. option D.

Arithmetic progression is the sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. The common difference is the value between each successive number in an arithmetic sequence

i.e. Common difference (d) = Successive term - Previous term

We have,

0, 5, 10, 15, 20, . . .

Here,

a₁ = 0

a₂ = 5

a₃ = 10

a₄ = 15

a₅ = 20

Now,

Find the common difference,

i.e.

Common difference (d) = a₂ - a₁ = 5 - 0 = 5,

Now,

Common difference (d) = a₃ - a₂ = 10 - 5 = 5

Now,

Common difference (d) = a₄ - a₃ = 15 - 10 = 5

Now,

Common difference (d) = a₅ - a₄ = 20 - 15 = 5

Now,

The Common difference is same for all i.e. 5.

Hence, we can say that the common difference of the given sequence will be 5, i.e. option D.

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[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$1040\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases} \\\\\\ 1040=1000(1+0.04t)\implies \cfrac{1040}{1000}=1+0.04t\implies \cfrac{26}{25}=1+0.04t \\\\\\ \cfrac{26}{25}-1=0.04t\implies \cfrac{~~\frac{26}{25}-1~~}{0.04}=t\implies \cfrac{~~\frac{1}{25}~~}{0.04}=t\implies 1=t[/tex]

Answer:

Properties of Real Numbers ...

Step-by-step explanation:

Commutative Property of Multiplication (Numbers) 2 • 10 = 10 • 2

Associative Property of Addition (Numbers) 5 + (6 + 7) = (5 + 6) + 7

Associative Property of Multiplication (Numbers) 6 • (3 • 2) = (6 • 3) • 2

Additive Identity (Numbers) 6 + 0 = 6

The equation demonstrates the Associative Property of Addition, stating that the grouping of numbers being added does not affect the sum.

The property shown in the equation 3 + (5 + 7) = (3 + 5) + 7 is the Associative Property of Addition. According to this property, the grouping of numbers being added does not affect the sum. In other words, when adding three or more numbers, it doesn't matter how they are grouped in parentheses.

In this specific equation, we are adding 5 and 7 first, which gives us 12. Then, adding 3 to 12 gives us a sum of 15. On the other side of the equation, we first add 3 and 5 to get 8, and then add 8 to 7 to get the same sum of 15.

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ANSWER

5.2387 and 5.2437

EXPLANATION

To round a decimal to the nearest hundredth means we should round to two decimal places.

To round to two decimal places we consider the third decimal place.

When we round 5.2387 to the nearest hundredth, we obtain 5.24 because the third decimal place is greater than or equal to 5 so we round up.

When we round 5.2437 to the nearest hundredth, we get 5.24 because the third decimal place less than 5 so we round off.

In fact there are infinitely many decimals that will round to 5.24 when rounding to the nearest hundredth.

For this case we have by definition, that each of the four internal angles of a square measure 90 degrees.

If we draw the diagonals of the square then the angles are divided by two, that is:

[tex]\frac {90} {2} = 45[/tex]

Thus, angle 3 measures 45 degrees.

[tex]A3 = 45[/tex]

By definition, the sum of the internal angles of a triangle is 180 degrees.

So:

[tex]A2 + A3 + 90 = 180\\A2 = 180-90-A3\\A2 = 180-90-45\\A2 = 45[/tex]

Thus, angle 2 measures 45 degrees.

Answer:

45 degrees

Answer:

Step-by-step explanation:

B

Answer:

Equation of line: y=3x-18

Step-by-step explanation:

Point: (5,7) and slope=-13

y-7=-13(x-5)

y=-13x+72

Answer:

16 quarters 2 dimes

Step-by-step explanation:

16 quarters is 4 dollars

2 dimes is 20 cents

Step-by-step explanation:

If D is number of dimes and Q is number of quarters:

D + Q = 21

10D + 25Q = 420

Solve the system of equations through either substitution or elimination.

10D + 25(21 - D) = 420

10D + 525 - 25D = 420

105 = 15D

D = 7

Q = 14

There are 7 dimes and 14 quarters.

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=6\\ \theta =\frac{\pi }{3} \end{cases}\implies s=6\left( \frac{\pi }{3} \right)\implies s=2\pi \implies \stackrel{\textit{rounded up}}{s=6.3}[/tex]

Answer: [tex]arc\ length=6.3\ ft[/tex]

Step-by-step explanation:

You  need to use the following formula for calculate the arc lenght:

[tex]arc\ length=r\theta[/tex]

Where  "r" is the radius and [tex]\theta[/tex] is the central angle in radians.

You know that the central angle in radians s:

[tex]\theta=\frac{\pi }{3}[/tex]

And the radius is:

[tex]r=6\ ft[/tex]

Therefore, the final step is to substitute the values into the formula. Then you get:

[tex]arc\ length=(6\ ft)(\frac{\pi }{3})[/tex]

[tex]arc\ length=6.3\ ft[/tex]