Solving a Quadratic Equation
Which statement is true about the equation (x – 4)(x + 2) = 16?
O The equation x – 4 = 16 can be used to solve for a solution of the given equation.
The standard form of the equation is x2 – 2x – 8 = 0.
O The factored form of the equation is (x + 4)(x – 6) = 0.
o One solution of the equation is x = -6.

Answer:

The 4th day so 21 miles the girls would have to run

Step-by-step explanation:

Answer:

Each girl would have ran a total of 21 miles and boys would have ran a total of 20 miles by the end of the fourth day before the couch order new javelins.

Step-by-step explanation:

Girls track team

First day of practice=3 miles

Days afterwards= 6 miles

Boys track team

Everyday= 5 miles

coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's.

First day

Each girl total mileage= 3 miles

Each boy total mileage= 5 miles

Second day

Each girl total mileage= 3miles+6miles=9 miles

Each boy total mileage=5 miles+5 miles= 10 miles

Third day

Each girl total mileage= 3+6+6=15 miles

Each boy total mileage=5+5+5=15 miles

Fourth day

Each girl today mileage= 3+6+6+6=21 miles

Each boy total mileage=5+5+5+5= 20 miles

Difference=girls-boys

=21-20= 1 mile

The fourth day is the day each girl's total mileage(21 miles) surpasses each boy's total mileage(20 miles) with a total of 1 mile

Answer:

[tex]\large\boxed{\sin\dfrac{2\pi}{3}=\dfrac{\sqrt3}{2}}[/tex]

Step-by-step explanation:

[tex]\sin\dfrac{2\pi}{3}=\sin\bigg(\pi-\dfrac{\pi}{3}\bigg)\\\\\text{use}\ \sin(x-y)=\sin x\cos y-\sin y\cos x\\\\=\sin\pi\cos\dfrac{\pi}{3}-\sin\dfrac{\pi}{3}\cos\pi\\\\\text{use the table from the attachment}\\\\\sin\pi=0\\\\\cos\dfrac{\pi}{3}=\dfrac{1}{2}\\\\\sin\dfrac{\pi}{3}=\dfrac{\sqrt3}{2}\\\\\cod\pi=-1\\\\\text{subtitute:}\\\\=(0)\left(\dfrac{1}{2}\right)-\left(\dfrac{\sqrt3}{2}\right)(-1)=\dfrac{\sqrt3}{2}[/tex]

The value of sin 2π/3 will be;

⇒ √3 / 2

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The expression is,

⇒ sin 2π/3

Now,

Since, The expression is,

⇒ sin 2π/3

⇒ sin 2×180/3

⇒ sin 120°

⇒ sin (90 + 30)°

⇒ cos 30°

⇒ √3 / 2

Thus, The value of sin 2π/3 = √3 / 2

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Answer:

The average power use is 806 watts....

Step-by-step explanation:

We all know that there are 31 days in May.

To find the total number of hours in 31 days, multiply the hours of one day by 31.

31*24 = 744 hours

Now we have given 600.kilowatt

To find average power, simply divide the given kilowatt by the total number of hours in 31 days.

= 600/744

Average power = 0.806 kilowatt

Since they have asked for the answer in watts we will convert kilowatt into watts.

We know that 1000 watts = 1 kilowatt, so we will multiply 0.806 by 1000 to convert it into watts

= 0.806*1000

= 806 watts.

Therefore the average power use is 806 watts....

Answer:

4/.5 = 8

Step-by-step explanation:

You can solve this by adding up .5 8 times to equal 4. Another way to look at it is that you have 4 individual pieces that are a foot long and you decide to split all of them in half. Let me know if you have any other questions.

Answer:

The equation that shows that is the division between 4 and 0.5 as:

[tex]\frac{4}{0.5}[/tex]

Step-by-step explanation:

First, it is necessary to know that one half foot is equivalent to 0.5 foot.

We can solve this using a rule of three in which we know that 1 piece has one half foot long, then 4 foot long how many pieces have. This is:

1 board -----------  0.5 foot

 X        ------------  4 foot

Where X is the number of pieces that he can get from a four foot long board.

Solving for X, we get:

[tex]X  = \frac{4*1}{0.5} = \frac{4}{0.5}[/tex]

So, the equation that shows how many one half foot pieces he can get from a four foot long board is:

[tex]X=\frac{4}{0.5}[/tex]

Answer:

C.WXYZ equal to PNLM

Step-by-step explanation:

Look at the given statement, WZYX is equal to PMLN.

WZYX is equal to PMLN.   W corresponds to P.

WZYX is equal to PMLN.   Z corresponds to M.

WZYX is equal to PMLN.   Y corresponds to L.

WZYX is equal to PMLN.   X corresponds to N

Now look in the choices. The letters must correspond like they do above.

W must correspond to P.

WXYZ equal to P...

X must correspond to N.

WXYZ equal to PN...

Y must correspond to L.

WXYZ equal to PNL...

Z must correspond to M.

WXYZ equal to PNLM

Answer: C.WXYZ equal to PNLM

Answer: C.WXYZ equal to PNLM

Answer:

P(S or T)= 3/4

Step-by-step explanation:

Given:

S and T are mutually exclusive events

find P(S or T)

P(S or T)= P(S) + P(T)

             = 1/3 +5/12

             =4+5/12

              =9/12

               =3/4 !

Answer:

The value of P(S or T) is 3/4.

Step-by-step explanation:

It is given that S and T are mutually exclusive events. It means intersection of S and T is 0.

[tex]S\cap T=0[/tex]

[tex]P(S\cap T)=0[/tex]

We need to find the value of  P(S or T). It means we have to find the probability of union of S and T.

[tex]P(S\cup T)=P(S)+P(T)-P(S\cap T)[/tex]

Substitute the given values in the above formula.

[tex]P(S\cup T)=\frac{1}{3}+\frac{5}{12}-(0)[/tex]

[tex]P(S\cup T)=\frac{4+5}{12}[/tex]

[tex]P(S\cup T)=\frac{9}{12}[/tex]

[tex]P(S\cup T)=\frac{3}{4}[/tex]

Therefore the value of P(S or T) is 3/4.

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================[/tex]

[tex]\text{We have}\ y=\dfrac{1}{5}x+10\to m_1=\dfrac{1}{5}\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{5}}=-5.\\\\\text{Put the value of a slope and the coordinates of the point (-3, 5)}\\\text{to the equation}\ y=mx+b:\\\\5=-5(-3)+b\\5=15+b\qquad\text{subtract 15 from both sides}\\-10=b\to b=-10\\\\\text{Finally:}\\\\y=-5x-10[/tex]

Answer:

[tex] 2x + 3 [/tex]

the sum of twice the number x and the number 3

[tex] x ^ 2 + y ^ 2 [/tex]

the sum of squares of the number x and the number y

[tex] 5x-2y [/tex]

the difference between five times more than the number x and twice the number y

[tex] x + 3x [/tex]

the sum of the number x and the number of triple x

[tex] \dfrac {ab} {3} [/tex]

the quotient of the product of the number a and the number b by the number 3

[tex] \dfrac {4x} {3y} [/tex]

the quotient of the product of the number 4 and the number x by the triple number y

[tex] \dfrac {m ^ 2} {n} +5 [/tex]

the sum of the quotient of the square of the number m by the number n and the number 5

[tex] 4-x [/tex]

the difference between the number 4 and the number x

[tex] p + 8q [/tex]

the sum of the number p and the product of the number 8 by the number q

[tex] n-6 [/tex]

the difference between the number n and the number 6

Answer:

1/8

Step-by-step explanation:

i added and combined like terms and got 1/8

Answer:   [tex]x[/tex] ≈ [tex]\±0.782[/tex]

Step-by-step explanation:

You need to solve for "x" in order to find its value.

 First, you need to apply the Negative exponent rule. This is:

[tex]a^{-n}=\frac{1}{a^n}[/tex]

 Then:

[tex]3x^{- 4}= 8[/tex]

[tex]\frac{3}{x^4}=8[/tex]

Now you can solve for "x":

 [tex]3=8x^4[/tex]

[tex]\frac{3}{8}=x^4[/tex]

Remember that:

[tex]\±\sqrt[n]{a^n}=\±a[/tex]

Then, you get:

[tex]\±\sqrt[4]{\frac{3}{8}}=x[/tex]

 [tex]x[/tex] ≈ [tex]\±0.782[/tex]

Answer:

The angle of descent of Artemis' plane is 6°

Step-by-step explanation:

Let

x -----> the angle of descent of Artemis' plane

we know that

The tangent of angle x is equal to divide the opposite side to angle x (altitude) by the adjacent side to angle x (horizontal distance)

see the attached figure to better understand the problem

so

tan(x)=2.2/22

x=arctan(2.2/22)=5.71°

Round to the nearest degree

x=6°

Answer:

The angle of descent of Artemis' plane is 6°

Step-by-step explanation:

Answer: 3/2 (simplified: 1.5)

Step-by-step explanation:

X=pi

X=3pi/2

Remove pi from both equations because pi will cancel out each other then you will be left with the equation 3/2. So therefore the rate of change would be 3/2 simplified would be 1.5

#2

Step-by-step explanation:

it is opening downwards so the number multiplying the function must be negative (in this case it is -2)

Answer:

y = -2(x -­ 1)² + 2

Step-by-step explanation:

recall that the vertex form of a quadratic equation is :

y = a(x - h)² + k, where (h, k) is the coordinate of the vertex (i.e maxima point)

from the graph we can see that the vertex is at x = 1, y = 2

hence the answers that are valid would have h = 1 and k = 2

right away by observing the answers, we can see that the last 2 choices have h = (-1) and so these are NOT the answers.

To decide between the first 2 choices, we observe from the given graph, that when x=0, y=0.

The only choice which satisfies this is the 2nd option

Proof:

for y = -2(x -­ 1)² + 2, when x = 0,

y = -2(0 -­ 1)² + 2

y = -2(-­ 1)² + 2

y = -2(1) + 2 = -2 + 2 = 0 (Proven to be valid)

Sanity check: check the first choice

y = (x ­- 1)² + 2

when x = 0,

y = (0- 1)² + 2

y = 1 + 2 ≠ 0 (not the answer)

Answer:

Step-by-step explanation:

David, if the problem came with possible answer choices, you need to share those choices.

The graph of f(x) = | x-1/4 | +4 stems from the graph of y = |x|, the absolute value function.  Draw this function; its vertex is at (0, 0) and it's v-shaped, opening upward.

First, translate this graph 1/4 unit to the right.  Second, translate the resulting graph 4 units upward.  Done.

Answer: A for plato users or edmentum

Step-by-step explanation:

[tex]g(2b)=5\cdot2b+3=10b+3[/tex]

The value of G(2b) = 10b + 3.

Given:

G(x) = 5x+3

To find:

the value of G(2b).

For G = 5x + 3

substitute x with 2b [tex]$=5 \cdot 2 b+3$[/tex]

Simplifying the above equation, we get

[tex]$5 \cdot 2 b+3: \quad 10 b+3$[/tex]

G(2b) = 10b + 3

Therefore, the value of G(2b) = 10b + 3.

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Answer:

A. 4 units

Step-by-step explanation:

Answer: B: 4 units

Step-by-step explanation:

the guy above me almost got it, lol, love u

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

The line crosses the y- axis at (0, 2) ⇒ c = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of line

Answer:

x + 2y = 4

Step-by-step explanation:

The y intercept (where it crosses the y axis) is (0,2)

Another point on the line is (4,0)

We can find the slope from these two points

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

   = (0-2)/(4-0)

   =-2/4 = -1/2

We have the slope and the y intercept

y = mx+b  where m is the slope and b is the y intercept

y = -1/2x +2

We want the equation of the line in standard form

Ax +By =C

Add -1/2x to each side

1/2x +y =  -1/2x +1/2x +2

1/2x +y =   2

Multiply by 2 because we do not want fractions

2(1/2x +y) = 2* 2

x + 2y = 4

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers

Step-by-step explanation:

Final answer:

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers have many interesting properties and applications in mathematics.

Explanation:

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it is a number that is only divisible by 1 and itself.

For example, the numbers 2, 3, 5, and 7 are prime numbers because they have no divisors other than 1 and themselves. On the other hand, the number 4 is not prime because it is divisible by 1, 2, and 4.

Prime numbers have many interesting properties and applications in mathematics, including their role in number theory and cryptography.

[tex]\bf \begin{cases} -7x+8y=1\\ 4x-8y=20 \end{cases}\qquad \qquad \stackrel{\textit{using elimination}}{ \begin{array}{llll} -7x~~\begin{matrix} +8y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=1\\ ~~4x~~\begin{matrix} -8y \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=20\\ \cline{1-1}\\ -3x~\hfill =21 \end{array}}[/tex]

[tex]\bf x=\cfrac{21}{-3}\implies \blacktriangleright x=-7 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting in the 2nd equation}}{4(-7)-8y=20}\implies -28-8y=20\implies -8y=48 \\\\\\ y=\cfrac{48}{-8}\implies \blacktriangleright y = -6 \blacktriangleleft[/tex]

The solution to the system is (x, y) = (-2.2, -1.8) the y-coordinate of the solution is -1, the correct option is A.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

The equations;

–7x + 8y = 1

4x – 8y = 20

Now,

To solve this system of equations, we can use the elimination method. We can multiply the first equation by 2 and add it to the second equation to eliminate y:

-14x + 16y = 2 +4x - 8y = 20

-10x = 22

x = -2.2

Now that we have x, we can substitute it into either equation to solve for y. Let’s use the first equation:

-7x + 8y = 1 -7(-2.2) + 8y = 1 15.4 + 8y = 1 8y = -14.4 y = -1.8

Therefore, the solution to the system of equations will be (x, y) = (-2.2, -1.8) the y-coordinate will be -1.

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Answer:

10(3/2x-22+3y)

Step-by-step explanation:

Answer:

Option B is correct.

Step-by-step explanation:

(x+2<5) U (x-7>-6)

Solving and finding the value of x and then taking Union of both answers

x+2 < 5

x < 5-2

x < 3

x-7 > -6

x > -6 + 7

x > 1

So, x < 3 or x > 1

{x|x<3 or x > 1}

Option B is correct.

Answer:

pi/2

Step-by-step explanation:

Arccos(tan(0))

Arccos( 0) since tan(0)=0

Arccos(0)=pi/2 since cos(pi/2)=0 and the restricted domain of cosine is [0,pi].

Answer:

1

Step-by-step explanation:

First of all go one step at a time. Find tan(0). For this question, you can use your calculator.

Tan(0) = 0 That's because the opposite side has a length of 0 and the tangent's definition is

Tan(x ) = opposite side / adjacent side. The opposite side and the adjacent side are part of the same length. There is no real opposite side.

=========

Now you are down to cos-1(0)

If you put that into your calculator like this

2nd Function

cos-1(

0

)

=

You will get 1

Answer:

(-2,-12), (-1,-6), (0,-3) and (1,-3/2)

Step-by-step explanation:

g(x) = -3(1/2)^x

Putting values of x

x     g(x)

-2    -3(1/2)^-2 = -12

-1     -3(1/2)^-1 = -6

0     -3(1/2)^0 = -3

1      -3(1/2)^1 = -3/2

Now, making the graph we will plot

(-2,-12), (-1,-6), (0,-3) and (1,-3/2)

The graph is shown in figure below.

To find g(x) values, substitute the x-values into the function equation. Calculate the result which gives you the y-value (g(x)) for each x-value. Plot these pairs of values on a graph to show the function's behavior.

To find the corresponding values of the function g(x), you need to substitute the x-values given into the function equation of g. For instance, if g(x) is a linear function given by y=3x+9, when x=1 the value of g(x) is 3*1+9=12, and this is the y-coordinate of the point plotted on the graph. Repeat this process with all the given x-values to get the corresponding y-values. Afterwards, plot all the (x, g(x)) pairs on the coordinate grid. The points are found at the intersection of the x and y (g(x)) values on the grid. After plotting, you can connect the points to give a graphical representation of the dependence of y on x.

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Answer:

[tex]\large\boxed{x^2-6x+9+x^2+2x-15=2x^2-4x-6}[/tex]

Step-by-step explanation:

[tex]x^2-6x+9+x^2+2x-15\qquad\text{combine like terms}\\\\=(x^2+x^2)+(-6x+2x)+(9-15)\\\\=2x^2-4x-6[/tex]

[tex]\huge\boxed{1 \frac{4}{5}\ \text{ft}}[/tex]

Change [tex]\frac{1}{5}[/tex] so that is has a common denominator.  [tex]\frac{1*2}{5*2}=\frac{2}{10}[/tex]

Make an equation.  [tex]\frac{7+7+2+2}{10}[/tex]

Add.  [tex]\frac{14+4}{10}[/tex]

Add.  [tex]\frac{18}{10}[/tex]

Divide both sides by 2.  [tex]\frac{9}{5}[/tex]

Convert to a mixed number.  [tex]1 \frac{4}{5}[/tex]

Answer:

1 4/5 ft.

Step-by-step explanation:

Change 7/10 into 70

Change 1/5 into 20

( It will be easier to find perimeter this way )

Formula: P=2(l+w)

P=2(l+w)=2·(70+20)=180

Then, you change the 180 back into a fraction to get 1 4/5.

Answer:

Option D) cos52 = x/24

Step-by-step explanation:

In this problem angle of 38 degrees and angle of 52 degrees are complementary angles

so

38°+52°=90°

therefore

cos(38°)=sin(52°)

we know that

see the attached figure with letters to better understand the problem

In the triangle ABD

cos(38°)=24/x ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse

Remember that

cos(38°)=sin(52°)

so

sin(52°)=24/x

In the right triangle ABC

cos(38°)=x/34 ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse

In the right triangle ABD

Applying the Pythagoras Theorem

[tex]BD=\sqrt{x^{2}-576}\ units[/tex]

[tex]cos(52\°)=(\sqrt{x^{2}-576})/x[/tex]----> The cosine of angle of 52 degrees is equal to divide the adjacent side to angle of 52 degrees by the hypotenuse

Answer:

Last choice. d.

Step-by-step explanation:

We are given the first term and the sixth term.

The first term is [tex]a_1=-9[/tex].

The sixth them is [tex]a_6=a_1r^5=-9216[/tex].

Let's solve for the common ratio, r.

[tex]-9r^5=-9216[/tex]

Divide both sides by -9:

[tex]r^5=1024[/tex]

Take the fifth root of both sides:

[tex]r=1024^{\frac{1}{5}}[/tex]

[tex]r=4[/tex]

So the common ratio is 4.

[tex]a_1=-9[/tex]

[tex]a_2=-9(4)=-36[/tex]

[tex]a_3=-9(4)^2=-144[/tex]

[tex]a_4=-9(4)^3=-576[/tex]

[tex]a_5=-9(4)^4=-2304[/tex]

[tex]a_6=-9(4)^5=-9216[/tex]

Answer:

75

Step-by-step explanation:

Geometric means you should think common ratio (words like multiplication or division).

First term=3

Second term=15

What can you multiply to first to give you second term? Please say 5! Yes 5! Why? Because 3*5=15.

So 5 is called the common ratio.  5 is the number that you will multiply to a term to find the very next term.

So the third term would be 15*5=75

The next value in the geometric sequence is 75.

A geometric sequence is a sequence of numbers in which each term can be found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, to find the next value in the sequence, we need to determine the common ratio. We can divide the second term (15) by the first term (3) to find the common ratio:

Common ratio = 15/3 = 5

Now that we know the common ratio is 5, we can find the third term in the sequence:

Third term = Second term × Common ratio = 15 × 5 = 75

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Answer:

yes

Step-by-step explanation:

6 times 6 = 36

Answer: Yes

Step-by-step explanation: Yes, it is a perfect square of 6. 6 x 6 = 36.

Answer:

[tex]x_1=x_2=-\dfrac{2}{3}[/tex]

Step-by-step explanation:

For the quadratic equation [tex]ax^2+bx+c=0[/tex] the discriminant is defined as

[tex]D=b^2-4ac[/tex]

and the quadratic formula for the roots gives us two roots:

[tex]x_1=\dfrac{-b-\sqrt{D}}{2a}[/tex]

and

[tex]x_2=\dfrac{-b+\sqrt{D}}{2a}[/tex]

For the equation [tex]9x^2 +12x+4=0[/tex] use quadratic formula to find roots:

[tex]D=12^2-4\cdot 9\cdot 4=144-144=0[/tex]

So,

[tex]x_1=x_2=\dfrac{-12\pm \sqrt{0}}{2\cdot 9}=-\dfrac{12}{18}=-\dfrac{2}{3}[/tex]