Mathematics High School

Which of the following is a factor of 6x2 + 2x − 21?

4x − 3
2x + 7
6x − 3
None of the above

Answers

Answer 1
ANSWER

None of the above

EXPLANATION

The quadratic expression given to us is

[tex]6 {x}^{2} + 2x - 21[/tex]

If the discriminant of this quadratic expression is a perfect square, then it has rational factors,

If we compare the above expression to the general quadratic expression,

[tex]a {x}^{2} + bx + c[/tex]
We have,
[tex]a=6,b=2,c=-21[/tex]


The discriminant is given by,

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

Thus

[tex] D = {2}^{2} - 4(6)( - 21)[/tex]


[tex] D = 4 + 504 = 508[/tex]

Since 508 is not a perfect square, the expression


[tex]6 {x}^{2} + 2x - 21[/tex]
has no rational factors.


Therefore D is the correct answer.

Related Questions

Outside a home, there is a 6-key keypad that can be used to open the garage if the correct four-digit code? is entered. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?

Answers

a) [tex]6^4=1296[/tex]

b)
[tex]|\Omega|=1296\\ |A|=1\\\\ P(A)=\dfrac{1}{1296}\approx0.08\%[/tex]

Answer:

The total number of codes is found with

[tex]P_{n}^{r} =n^{r}[/tex]

This formula is applied when we have to find combinations where the order matters, and each element can be used more than once, as happens with codes, there can be repetitions of numbers.

So, [tex]n[/tex] represents the total number of elements which are 6, and [tex]r[/tex] represents the total digits per code, which are 4.

Replacing these values, we have

[tex]P_{6}^{4} =6^{4}=1296[/tex]

This means there are 1296 possible codes.

Now, if the owner doesn't remember the code, the probability of entering the correct code on the first try would be

[tex]P=\frac{1}{1296}=0.0008 (or \ 0.08\%)[/tex]

This means that it's nearly impossible to enter the right code at once.

At a crime scene police find a person in Myrtle Beach shot while sunbathing on the pier. The pier is 20 feet high. The shot came 20 degrees from the parallel. How far was the shooter standing down the beach when the gun was fired?

Select one:
a. 30 feet away
b. 45 feet away
c. 55 feet away
d. 70 feet away

A person was hiking on a trail in Greenville County Park they were shot in the leg. Before he was shot, he had climbed to a height 45 vertical feet from the bottom of the mountain. The shooter was at angle of 40 degrees parallel to the mountain. How far was the shooter when he shot the person?

Select one:
a. 32 feet
b. 87 feet
c. 54 feet
d. 18 feet

A police officer shot a man running from a crime scene on a bridge that was 100 feet high. The bullet struck the victim 25 degrees to the parallel. Approximately how far away was the police officer when she fired her weapon?

Select one:
a. 500 feet
b. 380 feet
c. 217 feet
d. 78 feet

Answers

QUESTION 1 

The diagram to visualise this question is shown in the first picture below

We model this as a right angle triangle and we can use trigonometry ratio to find [tex]x[/tex] which is the distance between the shooter and the pier.

[tex]tan(x)= \frac{opposite}{adjacent} [/tex]
[tex]tan(70)= \frac{x}{20} [/tex]
[tex]x=20tan(70)[/tex]
[tex]x=54.94...[/tex] which rounded to 55 feet

QUESTION 2

Referring to the second diagram, we have
[tex]tan(x)= \frac{opposite}{adjacent} [/tex]
[tex]tan(50)= \frac{x}{45} [/tex]
[tex]x=45tan(50)[/tex]
[tex]x=53.6289....[/tex] which round to 54 feet

QUESTION 3

The length of [tex]x[/tex] is given
[tex]tan(x)= \frac{opposite}{adjacent} [/tex]
[tex]tan(65)= \frac{x}{100} [/tex]
[tex]x=100tan(65)[/tex]
[tex]x=214.45...[/tex] which round to 214

Answers:
Question 1 is C
Question 2 is C
Question 3 is [there is no option for 214 feet]

Triangle PIG was rotated to create triangle P'I'G'. Describe the transformation using details and degrees.

Answers

The rotation of the triangle is 270 degrees clockwise, or 90 degrees counterclockwise. Most commonly, clockwise measurements are used when it comes to rotations.

I hope this helped. Let me know if I was correct please.

Here is 1 red marble, 2 green marbles, and 5 blue marbles.you draw two marbles from the urn, but replace the first marble before drawing the second. find the probability that the first mable is blue and the second is green.

Answers

Total number of Marbles = 1 + 2 + 5 = 8
P(R) = 1/8
P(G) = 2/8 = 1/4
P(B) = 5/8
R = Event of picking a red marble
G = Event of picking a green marble
B = Event of picking a blue marble
The events are independent, i.e. the outcome of one trial will not affect the probabilities of the outcomes for another trial.
So, we can just multiply the P(B) by P(G) to find the desired overall outcome of the compound events:
5/8 * 1/4 = 5/32

How to solve piecewise functions step by step?

Answers

If you can graph a function, you can graph piecewise functions.  Each one of them is a different line or curve within the domain for that specific line of curve.  If the domain states it's less than or greater than a number, you circle that point on the line.  If the domain states it's also possibly equal to the point at the beginning or the end, you make a closed dot.  

I"m sure that's clear as mud, please respond with any additional questions.

(05.07 MC)

The net of a square pyramid is shown:

What is the surface area of the figure?

0.65 square inch
0.50 square inch
0.40 square inch
0.25 square inch

Answers

Answer:

  0.65 square inch

Step-by-step explanation:

Each triangle has an area given by ...

  A = 1/2bh = 1/2·(0.5 in)(0.4 in) = 0.10 in²

The square base has an area given by ...

  A = s² = (0.5 in)² = 0.25 in²

The total area is that of the square base and 4 triangles:

  S = 0.25 in² + 4×0.10 in² = 0.65 in²

Answer:

0.65 square inch

Step-by-step explanation:

A movie theater sold 1200 tickets and made $6400 in one night. If an adult ticket costs $7 and a children's ticket costs $3, how many adult tickets were sold?

A. a + c = 1200
7a + 3c = 6400
B. a c = 1200
7a 3c = 6400
C. a + c = 6400
7a + 3c = 1200
D. a + c = 10
7a + 3c = 7600

Answers

So the total number of movie tickets sold was 1200. This means that a + c = 1200 because a represents the number of adult tickets purchased and c represents the number of child tickets purchased. The total money they made off the movie was $6400. This means 7 multiplied by the number of adult tickets would result in the total they earned off adult tickets, and 3 multiplied by the number of child tickets would result in the total they earned off child tickets. This total equals 6400. So 7a + 3c = 6400. These are our two equations: a + c = 1200 and 7a + 3c = 6400. The answer choice that matches this is choice A, so your answer is A. Hope this helps. Feel free to ask more questions, or ask more questions about my explanation.

The data in the form of the equation can be written as a + c = 1200 and 7a + 3c = 6400. The correct option is A.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a movie theatre sold 1200 tickets and made $6400 in one night. If an adult ticket costs $7 and a children's ticket costs $3.

The expression in the form of the equation can be written as below,

a + c = 1200

7a + 3c = 6400

The correct system of equations will be option A.

To know more about an expression follow

https://brainly.com/question/29123054

#SPJ2

Solve the equation by completing the square. Round to the nearest hundredth if necessary x^2+3x=25

Answers

Answer:

The solutions are:  [tex]x= 3.72, -6.72[/tex]

Step-by-step explanation:

[tex]x^2+ 3x = 25\\ \\ x^2+3x+(\frac{3}{2})^2 = 25 +(\frac{3}{2})^2\\ \\ (x+\frac{3}{2})^2 = 25+\frac{9}{4}\\ \\ (x+\frac{3}{2})^2 =27.25\\ \\ \sqrt{(x+\frac{3}{2})^2} =\pm \sqrt{27.25} \\ \\ x+1.5= \pm \sqrt{27.25} \\ \\ x= -1.5 \pm \sqrt{27.25}\\ \\ x=-1.5+ \sqrt{27.25}=3.72015... \approx 3.72\\ \\ or\\ \\ x=-1.5-\sqrt{27.25} =-6.72015...\approx -6.72[/tex]

So, the solutions are:  [tex]x= 3.72, -6.72[/tex]


Derive the equation of the parabola with a focus at (2, –1) and a directrix of y = – .5

Answers

check the picture below...the parabola, with that focus point and that directrix.. .looks more or less like so

now, notice that, the directrix is above the focus, meaning the parabola is vertical and it opens downwards

the distance "p" is the same distance from the vertex to the directrix, since the vertex is half-way between those two fellows

now the  focus point is at 2,-1 and the directrix up above at +0.5, from -1 to 0.5 over the y-axis, there are 1.5 units, the vertex is half-way through, so 1.5/2 or 0.75

so the vertex is from -1 up 0.75 units, or from 0.5 down 0.75 units, that places it at -0.25, the axis of symmetry is x = 2, so, the vertex is at 2, -0.25

because the parabola is opening downwards, the value for "p" is negative, so, we know the distance "p" is 0.75, but because is an opening downwards parabola, then  p = -0.75

now, let's plug all those guys in, let's use for -0.25 then -1/4, and for -0.75 the -3/4, which is just the fraction version

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\[/tex]

[tex]\bf -------------------------------\\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \qquad \begin{cases} h=2\\ k=-\frac{1}{4}\\ p=-\frac{3}{4} \end{cases} \\\\\\ (x-2)^2=4\left( -\frac{3}{4} \right)\left( y-\left( -\frac{1}{4} \right) \right)\implies (x-2)^2=-3\left( y+\frac{1}{4} \right) \\\\\\ \cfrac{(x-2)^2}{-3}=y+\cfrac{1}{4}\implies \cfrac{(x-2)^2}{-3}-\cfrac{1}{4}=y \\\\\\ -\cfrac{1}{3}(x-2)^2-\cfrac{1}{4}=y[/tex]

(8.05)What conclusion can be determined from the dot plot below?

Answers

Most of the songs download in 10 seconds.

Answer:

the songs downloaded in  10 seconds

DEEZNUTS

Step-by-step explanation:

HELP ROUND 87671.5613658 TO THE NEAREST THOUSAND

Answers

since the 6 is in the hundreds place and it is above 5, then you round the thousands place up one to 88000

the question isssssssss

Answers

the answer to this problem is C
.5[tex] r^{2} [/tex] Θ = area of a sector
theta must be in radians not degrees though

someone help I don't get it

Answers

The answer is the first choice. 

What is best definition of combining like terms

Answers

they are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only like terms can be combined. We combine like terms to shorten and simplify algebraic expressions, so we can work with them more easily.

For the past two years Lynda Santana has recorded the costs of operating her car. They total $1,600 (fixed costs) and $2,134 (variable costs). She has driven a total of 14,000 miles. What was her cost per mile?

Answers

Total cost=fixed cost+variable cost
Total cost=1,600+2,134=3,734

Her cost per mile
3,734÷14,000=0.27 per mile

5 radians is the same as _____.

Answers

Answer:

286.5 degrees

Step-by-step explanation:

We want to change radians to degrees

2 pi radians = 360 degrees

5 radians * 360/ 2 pi

900/pi degrees

286.4788976 degrees

286.5 degrees

Answer: 286.48 degrees

Step-by-step explanation: We are trying to find the number of degrees. The equation to convert radians to degrees radian x 180/π. Plug in 5 for x.

5 x 180/π = 286.48

5 radians is the same as 286.48 degrees.

Point m is the midpoint of ab¯¯¯¯¯ . am=3x+3, and ab=8x−6. what is the length of am¯¯¯¯¯¯ ?

Answers

As given m is a midpoint of ab. So am is half of ab.

So we can write

[tex]am = \frac{ab}{2} [/tex]

As given am = 3x+3 , ab = 8x - 6.

So [tex]3x+3 = \frac{8x - 6}{2} [/tex]

[tex]3x+3 = \frac{2(4x - 3)}{2} [/tex]

[tex]3x+3 = 4x - 3[/tex]

[tex]3+3 = 4x - 3x [/tex]

[tex]6 = x[/tex]

So x = 6.

So length of am = 3x+3 = 3*6 + 3 = 21

help me please!! Find the measure of angle 2. Image attached

Answers

opposite angles = 180

180-49 = 131

 angle 2 = 131 degrees



A principal of $4700 is invested at 6% interest compounded annually. How much will the investment be worth after 12 years Use the calculator provided and round your answer to the nearest dollar.

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$4700\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &12 \end{cases} \\\\\\ A=4700\left(1+\frac{0.06}{1}\right)^{1\cdot 12}\implies A=4700(1+0.06)^{12}[/tex]

Which ordered pairs make both inequalities true? Check all that apply.
(–2, 2)
(0, 0)
(1,1)
(1, 3)
(2, 2)

Answers

Answer:

the answers are c and e 1,1 and 2,2

Step-by-step explanation:

Answer:

(1,1) (2,2)

Step-by-step explanation:

Let , −3−8 be a point on the terminal side of θ . find the exact values of sinθ , cscθ , and cotθ .

Answers

If ( -3, - 8 ) is the point on the terminal side of this angle:
cot (theta) = - 3/( - 8 ) =   3/8
cos (theta) / sin (theta) = 3/8
cos (theta) = 3 sin(theta)/8
sin² (theta) + cos² (theta) = 1
Therefore: sin ²(theta) + (3 sin(theta) /8 )² = 1
sin²(theta) + 9sin²(theta) / 64 = 1         /*64
64 sin² (theta) + 9 sin² (theta) = 64
73 sin² (theta) = 64
sin(theta) = √ (64/73) = - 8 / √73
csc (theta) = 1 / sin(theta) = 1 / (- 8/√73 ) = -√73 / 8

The exact values for sinθ, cscθ, and cotθ given the point (-3, -8) are sinθ = -8/√73, cscθ = √73/-8 (because sinθ and cscθ are negative in the third quadrant), and cotθ = 3/8 (positive since sin and cos signs cancel out).

The question involves finding the values of sinθ, cscθ, and cotθ given a point (-3, -8) on the terminal side of an angle θ. To find these values, we first need to determine the radius (r) of the corresponding right triangle formed by the point (-3, -8) and the origin (0, 0). The radius can be calculated using the Pythagorean theorem:

r = √((-3)2 + (-8)2) = √(9 + 64) = √73

Using the definitions of the trigonometric functions:

sinθ = opposite/hypotenuse = -8/√73cscθ = 1/sinθ = √73/-8cotθ = adjacent/opposite = -3/-8 = 3/8

Note that θ is in the third quadrant where both sine and cosine are negative; hence, sinθ and cscθ are negative, while cotθ is positive due to both the numerator and denominator being negative.

Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).

Answers

the answer:
the main formula of hyperbola is

(x-h)² / a² - (y-k)² / b² = 1, where the center is C (h,k)
and the vertex formmula is

(h+-a, k) and the covertex is (h, k+-b)

in our case vertices are already given:
(3, -1) and (3, -9)  so h+a =3  or  h - a =3 and k= -1, or k= -9
and co-vertices (-6. -5) and (12, -5)
h= -6  or h= 12, and  k+ b=-5, or k- b = -5
for example h= -6, h+a =3, a=3+6=9, k= -1, k+ b=-5 , we can get b= - 5 + 1 = - 4, so a=9, b=-4, h=-6, k= -1
the equation is
(x+6)² / 81 -  (y+1)² / 16 = 1, if the center is C(-6, -1)

the same method can be applied with the other choices of h and k.












Tom invests $200 into a bank account that yields 3.75 percent interest compounded daily. What will his exact account balance be after 2 years?

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 200
R interest rate 0.0375
K compounded daily 365
T time 2 years
A=200×(1+0.0375÷365)^(365×2)
A=215.58

Issac is standing 174 feet from the base of the South Carolina State House in Columbia. The angle formed by the ground and the line segment from his position to the top of the building is 46°. How tall is the SC State House? Round to the nearest foot.

Answers

The building would be 180 ft tall, rounded. 

Using the tangent function of trigonometry, the height of the South Carolina State House is calculated to be approximately 180.2 feet. When rounded, the building stands at an estimated 180 feet tall.

To calculate the height of the South Carolina State House, we can use trigonometry. Given that Issac is standing 174 feet from the base and the angle of elevation to the top of the building is 46°, we can use the tangent function to determine the height of the building. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the building in this case) to the adjacent side (the distance from Issac to the building).

Using the formula:

tangent (angle) = opposite/adjacent

The equation would be:

tangent (46°) = height of building / 174 feet

Solving for the height of the building:

height of building = 174 feet * tangent (46°)

Using a calculator with the tangent function:

height of building = 174 * 1.035530 (approx value of tangent (46°))

So:

height of building ≈ 180.2 feet

Rounded to the nearest foot, the height of the South Carolina State House is approximately 180 feet.



If 3 times a certain number is increased by 4 the result is 28. What is the number?

If x is "the number," which of the following equations could be used to solve for the number?

c.3x + 4 = 28

b.3(x + 4) = 28

a.3x = 4 + 28

Answers

x = number

the equation to use is: 3x+4=28


3x+4=28

3x=24

x-24/3 =8

x=8


Solve for x: 3/4x+5/8=4x


x = __________________ Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar.

Answers

So, you have 3/4x + 5/8 = 4x. We can do this in two ways. Since fractions are harder to deal with, we can turn the fractions into whole numbers.

First we need to find the LCD (Least Common Denominator) between 4 and 8, which is 8. So multiply the 3/4x by 2/2, which gives you an equivalent fraction of 6/8x.

So now we have 6/8x + 5/8 = 4x. Now multiply both sides by 8, to get rid of the denominators of the fractions. That gives us 6x + 5 = 32x. Now use the subtraction property of equality to subtract 6x from both sides giving us 5 = 26x. 

Now you can use the division property of equality to divide 26 on both sides, which gives us x = 5/26.

Hope this helps. :D Feel free to ask any other questions, and if you have any questions about my explanation, don't hesitate to ask.

Solve 3(2x - 4) < 2(x + 4)

Answers

6x - 12 < 2x + 8
4x < 20
x < 5

Use the graph below to fill in the blank with the correct number:

f(−2) = _______


Numerical Answers Expected!

Answer for Blank 1:

Answers

If you have f(-2), you are expected to sub in -2 for x to find out the y value at that x value. Find -2 on the graph and see what y is at that point. y is 2, therefore, f(-2) = 2.

Type the correct answer in the box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar. Simplify the expression. tan(-x) cos(-x) =

Answers

THE ANSWER IS : sin(-x)

Answer:

The correct simplification of the given expression  [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].

Step-by-step explanation:

The given expression is:

[tex]tan(-x){\times}cos(-x)[/tex]

Now, simplifying the above given expression, we get

=[tex]\frac{sin(-x)}{cos(-x)}{\times}cos(-x)[/tex] (because [tex]tanx=\frac{sinx}{cosx}}[/tex])

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

Also, we know that [tex]sin({-\theta})=-sin{\theta}[/tex], tehrefore teh expression becomes

=[tex]-sinx[/tex]

Hence, the correct simplification of the given expression  [tex]tan(-x){\times}cos(-x)[/tex] is [tex]-sinx[/tex].

The length of a rectangle is 4 cm greater than its width. the perimeter is 32 cm. find the length of the rectangle. 12 cm 18 cm 10 cm 6 cm

Answers

So say the width of the rectangle is x, then the length would be x + 4 as it's 4cm greater. So you add all of the sides and you get 4x + 8 = 32
Subtract 8 from both sides and you're left with 4x = 24.
Divide both sides by 4 to get the value of x which is 6.
6 + 4 = 10.
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