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In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?

Answer:

The answer to this question is True

Answer: true

Step-by-step explanation:

Answer:

1)

[tex] \frac{26 + 16 + 11 + 13 + 24}{5} = \frac{90}{5} = 18[/tex]

2)

[tex] \frac{51 + 20 + 32 + 18 + 45 + 8}{6} = \frac{174}{6} = 29[/tex]

3)

[tex] \frac{17 + 39 + 15 + 42 + 37 + 61 + 19 + 40}{8} = \frac{270}{8} = 33.75[/tex]

4)

[tex] \frac{62 + 21 + 18}{3} = \frac{101}{3} = 33.67[/tex]

5)

[tex] \frac{9.2+8.6+9.4+9.2}{4} = \frac{36.4}{4} = 9.1[/tex]

$0.30 (farmer's market) < $0.35 (grocery store), the farmer's market offers blueberries at a lower price per ounce.

To compare the cost of blueberries from a grocery store and a farmer's market below:-

Cost of blueberries at the grocery store:

Cost of blueberries at the farmer's market:

Thus,

Answer:

[tex]\frac{1}{x^2y^6}[/tex]

Step-by-step explanation:

We are given [tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex]

First rule I'm going to use is [tex](m^rn^p)^s=m^{r \cdot s}n^{p \cdot s}[/tex].

This gives us:

[tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex] is

[tex](x^2y^6) \cdot (x^{-4}y^{-12})[/tex].

Now pair up the bases that are the same:

[tex](x^2x^{-4}) \cdot (y^6y^{-12})[/tex].

Add the exponents when multiplying if the bases are the same:

[tex]x^{-2} \cdot y^{-6}[/tex]

Now usually teachers don't like negative exponents.

To get rid of the negative exponents just take the reciprocal:

[tex]\frac{1}{x^2} \cdot \frac{1}{y^6}[/tex]

[tex]\frac{1}{x^2y^6}[/tex]

The algebraic expression 3y+1 has a term with a coefficient of 3.

A coefficient is a constant value accompanying a variable that is multiplied by it. For example, 2 is the coefficient of x in 2x.

We can evaluate the given options.

In Option A, we have 3y+1. Here the expression has a term with a coefficient of 3.

In Option B, we have -2y + 5+ 3. Here the expression does not have a term with a coefficient of 3.

In Option C, we have 5y-7. Here the expression does not have a term with a coefficient of 3.

In Option D, we have 3(y-6). Here the expression does not have a term with a coefficient of 3.

Therefore, we have found that the algebraic expression 3y+1 has a term with a coefficient of 3.

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Answer:

[tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

To find the slope of a line using two points, employ the use of the slope formula.

[tex]\frac{y_{2}-y_{1}}{x_{2}- x_{1}}[/tex]

Your y1 term is -2, your y2 term is -3.

Your x1 term is -3, your x2 term is 0.

[tex]\frac{-3-(-2)}{0-(-3)} \\\\\\\frac{-3+2}{0+3} \\\\\frac{-1}{3} \\[/tex]

The answer is:

The quadratic function that fits the given picture is:

[tex]y=-3x^{2}+13x-5[/tex]

We can solve the problem and find the correct function that fits the curve below by finding which function intercepts the y-axis at -5 (we can see it from the picture), also, we need to look for a function that represents a parabola opening upwards. We need to remember that when a parabola is opening upwards, its quadratic term coefficient is negative.

So, we can see that from the given functions, the only function that represents a parabola opening upwards and its y-intercept is located at y equal to -5 is the second option:

[tex]y=-3x^{2}+13x-5[/tex]

We have that :

[tex]a=-3(negative)\\b=13\\c=-5(y-intercept)[/tex]

We can see that the quadratic term (a) is negative, and the quadratic function intercepts the y-axis at y equal to -5.

Hence, the answer is:

The quadratic function that fits the given picture is:

[tex]y=-3x^{2}+13x-5[/tex]

Have a nice day!

Note: I have attached a picture for better understanding.

Answer:

1,440

Step-by-step explanation:

1.5 percent of 96k

Answer:

36

Step-by-step explanation:

I think it may be 36. I did 6×6, but I'm not fully positive

There are 720 different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster.

To calculate the number of different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster, we can use the concept of permutations.

Since each friend occupies one seat and no two friends can occupy the same seat, we have 6 choices for the first seat, 5 choices for the second seat, 4 choices for the third seat, and so on until 1 choice for the last seat.

So, the total number of arrangements is the product of these choices:

[tex]\[ 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]

Answer:

Option C and D are correct options

Step-by-step explanation:

The correct options are C and D.

We know that i = √-1

i² = -1

i³ = -i

and i^4 = 1

Lets solve the options one by one:

i^6 =1

Break the power:

i² *i ² * i² = (-1)(-1)(-1)

= -1

Therefore A is wrong

B) i^18 = 1

Lets break the power:

i²* i² *i² *i²*i²*i²*i²*i²*i²

put the value of i^2

= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)(-1)

= -1

Therefore option B is incorrect.

C) i^7 = -i

= i² * i² *i² *i

=(-1) (-1) (-1) * √-1

= - √-1

We know that √-1 = i

So,

- √-1 = -i

Therefore option C is correct.

D) i^16 = 1

= i² * i² * i² * i² * i² * i² *i² *i²

= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)

= 1

Therefore option D is correct.

Thus option C and D are correct option....

Answer: Option C and Option D

Step-by-step explanation:

Remember that by definition we have to:

[tex]i=\sqrt{-1}[/tex] and [tex]i^2=-1[/tex]

So for the option A we have to:

[tex]i^6=(\sqrt{-1})^2*(\sqrt{-1})^4\\\\i^6=-1*(-1)^2\\\\i^6=-1[/tex]

Option A is false

So for the  option B we have to:

[tex]i^{18}=(i^6)^3[/tex]

We know that [tex]i^6=-1[/tex]

So

[tex]i^{18}=(-1)^3[/tex]

[tex]i^{18}=-1[/tex]

Option B is false

So for the option C we have to:

[tex]i^7=(i)^6*i^1[/tex]

[tex]i^7=-i[/tex]

Option C is true

Finally for the option D we have to:

[tex]i^{16}=(i^4)^4[/tex]

[tex]i^{16}=((-1)^2)^4[/tex]

[tex]i^{16}=(1)^4[/tex]

[tex]i^{16}=1[/tex]

Option D is true

To find the slope of a line you must do [tex]\frac{rise}{run}[/tex]

Look at the image to find the rise (in pink) and run (in green) on the graph:

In this case the rise is 3 and the run is -4 (the reason the four is negative is because it "runs" to the left, which is the negative direction of the coordinate plane) so the slope of this line is:

[tex]\frac{-3}{4}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Continuous because there are no breaks.

The graph is included as an attachment.

Step-by-step explanation:

Alright we want to graph:

y=x-4 for x<2

y=-2x+2 for x=2 or x>2

So let's graph the first piece y=x-4 for x<2.

I'm going to plug in 2 for x:   y=2-4=-2.   So this one line is going to contain an open circle at (2,-2). I say open circle because we did not have that we could actually include x=2 here because it says for x less than 2.

Now we are going to enter in one more number less than 2....your choice.

Let's go with x=0. When you plug in 0 for x into y=x-4 you get y=0-4=-4. So our line is going to include (0,-4).

So we are going to graph the points (0,-4) and (2,-2) again where (2,-2) is an open circle.  Connect these points. You may extend your line left because we have x<2, but do not extend it right of x=2.

Let's look at the other piece now: y=-2x+2 for x=2 or x>2.

I'm going to plug in 2 for x:  y=-2(2)+2=-4+2=-2 so we are going to include the point (2,-2) on our line.  This was actually a point we used from above that we didn't want to include.  We do now want to include because of the x=2 in our inequality so the dot can now be filled in. We need one more point to graph this line.  Let's plug in a number greater than 2 since our inequality say x=2 or x>2.  You choose.  How about x=3?

y=-2(3)+2=-6+2=-3.   So we are going to include the point (3,-3). So starting at (2,-2) and going right to connect it to (3,-3), you could extend passed the (3,-3) to the right.

I will show you my graph.

There are no breaks in the "curve", so it is continuous for all real numbers.

Answer:

"number line with open circles on negative 9 and 5, shading going in the opposite directions."

Step-by-step explanation:

Your inequality doesn't include an equal sign so there will be no closed holes. It will only be open holes.

|u|>14 means that the number u has to be greater than 14 or less than -14.  These numbers I describe just now all have a distance greater than 14 from 0.

So |u|>14 implies u>14 or u<-14.

But we are solving |2x+4|>14 so this implies we have 2x+4>14 or 2x+4<-14.

2x+4>14

Subtract 4 on both sides:

2x    >10

Divide both sides by 2:

x      >5

2x+4<-14

Subtract 4 on both sides:

2x    <-18

Divide both sides by 2:

x      <-9

So our solution is x>5 or x<-9.

Graphing!

~~~~~~~O                                         O~~~~~~~~

-----------(-9)---------------------------------(5)---------------

So we shaded to the right of 5 because our inequality says x is bigger than 5.

We shaded to the left of -9 because our inequality says x is less than -9.

Answer:

x=-2.5 if the function is [tex]f(x)=\frac{8x-3}{-4x-10}[/tex]

Step-by-step explanation:

[tex]y=\frac{8x-3}{-4x-10}[/tex] has discontinuities when the denominator is 0.

You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.

That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.

If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.

Let's do this now.

When is -4x-10 equal to 0?

We have to solve the equation:

-4x-10=0

Add 10 on both sides:

-4x=10

Divide both sides by -4:

x=10/-4

Reduce by dividing top and bottom by 2:

x=5/-2

x=-5/2

or

x=-2.5  (if you want decimal form)

Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.

Let's see.

8(-2.5)-3=-23

Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.

If the top were 0, then you would have had a hole at x=-2.5.

Answer:

y-2 = 1/4(x-20)  point slope form

y = 1/4x -3  slope intercept form

Step-by-step explanation:

y = -4x

The slope is -4

The slope that is perpendicular is the negative reciprocal

- (1/-4) = 1/4

The slope of our new line is 1/4

We have a point and the slope, so we can use point slope form

y-y1 = m(x-x1)

y-2 = 1/4(x-20)

If we want the line in slope intercept form, distribute

y-2 = 1/4x -5

Add 2 to each side

y-2+2 = 1/4x -5+2

y = 1/4x -3

Answer:

x=-2

Step-by-step explanation:

-9x+1=-x+17

Add 9x on both sides:

     1=8x+17

Subtract 17 on both sides:

   -16=8x

Divide both sides by 8:

     -2=x

Check x=-2!

-9x+1=-x+17     with x=-2

-9(-2)+1=-(-2)+17

18+1=2+17

19=19

19=19 is a true equation so x=-2 is correct.

Answer: b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Josh has to drive at least 6 hours.                 d≥ 6 Answer 2

Amelia walking 35 min or less                       b ≤ 35 Answer 3

Nancy < 35 hours = part time                         y < 35 Answer 1

Sarah at least 6 hours math                           f > 6 Answer 4

Answer:

15 pounds

Step-by-step explanation:

5 bags @ 3 pounds

5 x 3 = 15 lbs.

Samuel has 5 bags of almonds, each weighing 3 pounds. By multiplying the number of bags by the weight of each bag (5 * 3), we find that Samuel has a total of 15 pounds of almonds.

The total weight of Samuel's 5 bags of almonds is:

Multiply the weight of a full bag (3 pounds) by the number of bags (5): 3 pounds/bag x 5 bags = 15 pounds

Therefore, Samuel has 15 pounds of almonds.

To find the number of miles Lissette biked, the provided information leads to an algebraic equation where Lissette's distance is represented as 'x' and Shane's as '3x + 1', combining to equal 7 miles.

The subject of this question is mathematics, specifically algebra, where you need to write an equation based on a word problem.

The problem states that Shane biked 1 mile more than three times the number of miles Lissette biked, and their combined total is 7 miles. If we let x represent the number of miles Lissette biked, then Shane biked 3x + 1 miles. The equation to determine the number of miles Lissette biked is:

x + (3x + 1) = 7

Answer:

Step-by-step explanation:

The point-slope of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the poinys (-1, -10) and (5, 2). Substitute:

[tex]m=\dfrac{2-(-10)}{5-(-1)}=\dfrac{12}{6}=2[/tex]

Put the value of the slope and the coordinateso f the point (5, 2), to the equation of a line:

[tex]y-2=2(x-5)[/tex]

In the question we have y - 6 = ...

Therefore

[tex]y-2=2(x-5)[/tex]    subtract 4 from both sides

[tex]y-6=2(x-5)-4[/tex]          use the distributive property

[tex]y-6=2x-10-4[/tex]

[tex]y-6=2x-14[/tex]      distributive

[tex]y-6=2(x-7)[/tex]

Answer:

The answer is 6.

Step-by-step explanation:

A fifth of 10, or 10 divided by 5, is 2. Two is a third of 6. Therefore, the answer must be 6.

The number whose one - third is equal to one - fifth of 10 is 6.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a number such that one - third of it is equal to a one - fifth of 10.

Assume that the number is [x].

Then, one - third of the number = 1/3 of x = x/3

Now, one - third of the number = one - fifth of 10, so we can write -

x/3 = 1/5 of 10

x/3 = 1/5 x 10

x/3 = 10/5

x = 10/5 x 3

x = 6

The number is 6.

Therefore, the number whose one - third is equal to one - fifth of 10 is 6

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Answer:

Hi there!

The answer to this question is: C. 14

Step-by-step explanation:

Using the formula for sine I solved the missing side.

sin(62)= 12/x

then you need to solve for x

x= 12/ sin(62)

and you get 13.59 so round up to get 14

The length of the third side of a triangle is 16.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Use the Law of Cosine to find the third side of the triangle.

Law of Cosine is given by

[tex]$$a^{2}=b^{2}+c^{2}-2 b c$$[/tex]

Substituting the known values, we get

[tex]$$a^{2}=12^{2}+19^{2}-2 \cdot 12 \cdot 19 \cos 56$$[/tex]

By simplifying, we get

[tex]&a^{2}=505-456 \cos 56 \\[/tex]

[tex]&a^{2}=250.008 \\[/tex]

[tex]&a=15.81[/tex]

When rounded to the nearest whole number, the length of the third side is 16.

The length of the third side of a triangle is 16.

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Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

Answer:

CDE

Step-by-step explanation:

Answer:

1. the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. 2x+2.1=7.5

Step-by-step explanation:

Given:

1.

A scalene triangle with sides y, 4y and x

and perimeter,p= 60cm

As per perimeter formula:

p= sum of all sides

Putting values we get

60=x+4y+y

60=x+5y

so correct options are

the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. An isosceles triangle with sides y=2.1, x and x

and perimeter,p = 7.5

As per perimeter formula:

p= sum of all sides

Putting values we get

7.5=2.1 + x +x

7.1=2.1+2x !

Answer:

                 -8

If cot Ф = ------

                  3

Step-by-step explanation:

Justine, when you're given answer choices, please share them.  Thank you.

                 -3

If tan Ф = ------

                  8

then:

                 -8

If cot Ф = ------

                  3

Answer:

∛x²-8 = 2

-2∛x² = 2

∛x² = 2+2

x² = 4³

x = √64

x = 8

Answer:

C. x = –4 or x = 4

Step-by-step explanation:

B. s = 7 (for the second one)

Answer:

Kerry donated $50 to a charity.

Step-by-step explanation:

500/10=50

Answer:

$50

Step-by-step explanation:

1/10 of $500 =

= 1/10 * $500

= $500/10

= $50

Answer:

This relation is a function.

Step-by-step explanation:

A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.

We have

{(-3, -6), (-1, -6), (5, -6), (8, -6)}

x = -3 → y = -6

x = -1 → y = -6

x = 5 → y = -6

x = 8 → y = -6

YES. This relation is a function.

/each x has one value of y/

Answer: Yes, it is a function

Step-by-step explanation:

Answer:

14x-10y=-96

Step-by-step explanation:

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

so

we have

y=1.4x+9.6

Multiply by 10 both sides

10y=14x+96

isolate the variable x and y (Remember that A must be positive)

14x-10y=-96 -----> standard form

Answer:

cos theta = -4/5.

sec theta = -5/4.

tan theta = 3/4.

cot theta = 4/3.

Step-by-step explanation:

sin^2 theta + cos^2 theta = 1

(-3/5)^2 + cos^2 theta = 1

cos^2 theta = 1 - 9/25

cos^2 theta = 16/25

cos theta = -4/5 (negative because  it is in Quadrant 3).

sec theta = 1 / cos theta = -5/4.

tan theta = sin theta / cos theta = -3/5 / - 4/5

= -3/5 * -5/4

=  3/4.

cot theta  =  1 / tan theta = 4/3.

The other trigonometric functions can be found using the Pythagorean Identity and the definitions of the trigonometric functions. The values are cos theta = -4/5, tan theta = 3/4, csc theta = -5/3, sec theta = -5/4, and cot theta = 4/3.

The given values are sin theta = -3/5 and cos theta = -5/3, which are located in quadrant 3. In this quadrant, sine and cosine are both negative. To find the values of the other trigonometric functions, we will use the Pythagorean Identity and the definitions of the trigonometric functions.

We can find cosine through the Pythagorean Identity, sin² theta + cos² theta = 1. Solving for cos theta, we get cos theta = sqrt(1 - sin² theta) = sqrt(1 - (-3/5)²) = -4/5. Note the negative sign since we are in quadrant 3.

Next, we can find tan theta = sin theta/cos theta = (-3/5) / (-4/5) = 3/4.

For the reciprocal functions, we have csc theta = 1/sin theta = -5/3, sec theta = 1/cos theta = -5/4, and cot theta = 1/tan theta = 4/3.

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