Find the Vertex of the function glven below?
y = x^2-4x+1

Answer:

Original Price = $500

Step-by-step explanation:

The discount is 36%

and the discount amount is $180

Thus,

we can say that 180 is 36% of what number?

We let that number be "x" (original price). So we can say:

180 is 36% of x

In equation that will be:

180=36%*x

180=(36/100)*x

180=0.36x

So,

x = 180/0.36

x = $500

This is the original price.

Answer:

Y<4 or y>9

Hope this helps you out!

Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times  the number of adult tickets sold on Friday  

                             =  1,678 x 2  = 3,356

Children's Tickets sold = 3 times the number of children's tickets sold on Friday.

=  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938.

Answer:

3

Step-by-step explanation:

15 fish / 5 days = 3 fish per day

Answer:

3

Step-by-step explanation:

15 fish / 5 days = 3 fish per day

Answer:

B-How many books have each of my classmates read this year?

Step-by-step explanation:

Every year the number of books each classmate read would be different

Answer:

b

Step-by-step explanation:

Answer:

B(6, - 11 )

Step-by-step explanation:

Since the translation rule is (x - 2, y + 3 )

Then to go back the way do the opposite, that is

(x + 2, y - 3 ), thus

B(4 + 2, - 8 - 3 ) → B(6, - 11 )

Answer:(6, -11)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

For the arcs WX and YZ to be congruent.

The angles subtended at the centre of the circle must be congruent.

This is not the case here as arc WX subtends 80° and arc YZ subtends 35°

Thus arc WX and arc YZ are not congruent.

Answer:

48 will be the answer.

Step-by-step explanation:

we can simply find the 80 percent of 60.

80 * 60 / 100 = 4800/100 = 48.

so 48 students think he is their favorite teacher.

Answer:

Question 1)

Rearrange 2x-6y=12 to slope-intercept form by isolating y

y = (1/3)x - 2

Sub each x value to get the y value

x       y

-3     -3

0      -2

3      1

6      0

y = (1/3)x - 2

y = (1/3)(-3) - 2

y = -3

Point (-3, -3)

y = (1/3)x - 2

y = (1/3)(0) - 2

y = -2

Point (0, -2)

y = (1/3)x - 2

y = (1/3)(3) - 2

y = 1

Point (3, 1)

y = (1/3)x - 2

y = (1/3)(6) - 2

y = 0

Point (6, 0)

See graph below

Question 2)

a) No, each support does not have the same starting coordinates. For example, the first support from the left starts at (0,0) and the second support from the left starts at (2,1).

b) No, each support does not have the same ending coordinates. For example, the first support from the left ends at (2,1) and the second support from the left ends at (6,3).

c) No, each support does not have the same change in x-values from the start to end.

The first support starts at the x-value 0 and ends at the x-value 2. It increased by 2.

The second support starts at the x-value 2 and ends at the x-value 6. It increased by 4.

d) No, each support does not have the same change in y-values from the start to end.

The first support starts at the y-value 0 and ends at the x-value 1. It increased by 1.

The second support starts at the y-value 1 and ends at the x-value 3. It increased by 2.

e) Yes, each support has the same change in the ratio of y-values over x-values. For the first support, the change is y-values is 1 and the change in x-values is 2. (1/2)

For the second support, the change in y-values is 2 and the change in x-values is 4. (2/4 = 1/2)

They both have the ratio of change in y-values over x-values 1/2.

Answer:

4.23 * 10³ = 4.23 * 1000 = 4,230

Step-by-step explanation:

We should know that;

10³ = 10 * 10 * 10 = 1000

∴ 4.23 * 10³ = 4.23 * 1000 = [tex]\frac{423}{100}*1000[/tex] = 4,230

Answer:

4.23 * 10³ = 4.23 * 1000 = 4,230

Step-by-step explanation:

Answer:

The number of green marbles are 36.

Step-by-step explanation:

Given:

Total number of marble bag contains is 42.

The number of green marbles is 6 more than 5 times the number of red marbles.

Let the number of red marbles be [tex]x[/tex].

So, the number of green marbles = [tex]6+5x[/tex]

Now, to get the number of green marbles.

According to question:

[tex]x+(6+5x)=42[/tex]

[tex]6x+6=42[/tex]

Subtracting 6 in both sides :

[tex]6x+6-6=42-6[/tex]

[tex]6x=36[/tex]

Now, by dividing 6 on both sides:

[tex]6x\div 6=36\div 6[/tex]

[tex]x=6[/tex]

The number of red marbles are 6.

And, the number of green marbles are [tex]6+5x[/tex]

                                                                 = [tex]6+5\times 6[/tex]

                                                                 =[tex]6+30[/tex]

                                                                 = [tex]36[/tex]

Therefore, the number of green marbles are 36.

Answer:

45 cats 18 dogs

Step-by-step explanation:

63/7 = 9

9*5=45

9*2=18

45+18=63

The number of cats up for adoption is 45.

Given that, the ratio of cats to dogs=5:2.

The total number of cats and dogs up for adoption is 63.

In mathematics, a ratio indicates how many times one number contains another.

Now, 5+2=7

Number of cats=5/7×63=45

Therefore, the number of cats up for adoption is 45.

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Answer:

Yes

Step-by-step explanation:

the total discount allowed will be 25% of the original price and futher 10% of the original price which will amount to 10%+25% and this equal 35%

Answer:

4.  35 times larger

Step-by-step explanation:

Doing Question #4 Only

4.

Before we see this problem's solution. Lets get a background.

Suppose something has an area of "A" sq. meters.

and

Suppose another land has an area of "B" sq. meters.

and suppose A > B

If we want to know how many times A is larger than B, we simply have to divide the larger one (A) by the smaller one (B).

Now, onto our question:

We want to know how many times larger the national is than state park. So we divide the area of national by the area of state. That would be:

[tex]\frac{7*10^8}{2*10^7}[/tex]

Since the numbers are in scientific notation, we look at the rule below on how to divide scientific notation numbers:

[tex]\frac{a*10^b}{c*10^d}=(\frac{a}{c})*10^{b-d}[/tex]

Now, we apply the rule:

[tex]\frac{7*10^8}{2*10^7}\\=\frac{7}{2}*10^{8-7}\\=3.5*10^1\\=3.5*10\\=35[/tex]

So, the national park is 35 times larger than the state park.

Answer:

h = 1.4

c = 2.8

Step-by-step explanation:

For each problem, remember the special triangle side ratios then use a proportion. To solve, isolate the variable.

For the triangle with the variable h:

Since two of the angles are 45, this is an isosceles triangle. All isosceles triangles have two equal sides that are not the hypotenuse.

In a right isosceles triangle, the ratio for regular side to hypotenuse is 1 to √2.

[tex]\frac{1}{\sqrt2} =\frac{h}{2} \\h = 2\frac{1}{\sqrt2} \\h = \frac{2}{\sqrt2} \\h = \frac{2\sqrt2}{2} \\h = \sqrt{2}[/tex]

h = √2

h ≈ 1.4

For the triangle with the variable c:

The is an equilateral triangle cut in half because the angles are 30 and 60.

The side ratio of altitude to hypotenuse is √3 to 2.

[tex]\frac{\sqrt{3} }{2} =\frac{c}{4} \\\sqrt{3} = \frac{c}{2}\\2\sqrt3 = c[/tex]

c = 2√2

c ≈ 2.8

Answer:

Hey.

By what percentage was the price of the video games reduced ?

By 25%.

Step-by-step explanation:

$60 is the 100% price.

Now we have to find what percentage belongs to the reduced price, $45.

45×100/60 = 75.

75% is the percentage of the reduced price.

We can find the difference between them by doing a substraction.

100%-75% = 25%.

Hope I helped you !

We can't really use w = 1 in this equation because it would be a false equation.

3w = 84

3(1) = 84

3 ≠ 84

If we were to solve for w then we can divide 3 to both sides.

3w = 84

3w/3 = 84/3

w = 28

______

Best Regards,

Wolfyy :)

Hey there!

3w = 84

DIVIDE 3 to BOTH SIDES

3w/3 = 84/3

CANCEL out: 3/3 because it give you 1

KEEP: 84/3 because it give you the w-value

NEW EQUATION: w = 84/3

SIMPLIFY IT!

w = 28

Therefore, your answer is: w = 28

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

In simple terms, absolute value makes a negative number positive. So, |ab| simplifies to -ab when a<0 and b>0, |2b| simplifies to -2b when b<0, and |c| simplifies to -c when c<0.

The expression |ab| simply represents the absolute value of the product of a and b. Absolute value is a mathematical function that determines the distance of a number from zero. In this case, as a is less than 0 (negative) and b is greater than 0 (positive), the product ab would be negative. But absolute value always returns a positive output or zero, so, |ab| would be -ab because absolute value would remove the negative sign.

The expression |2b|, where b is less than 0, would simplify to -2b, as b is negative so absolute value removes the negative sign.

Lastly, the expression |c|, when c is negative, simplifies to -c as the absolute value would remove the negative sign from c.

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Final answer:

To simplify expressions with absolute value signs, one must take into account the sign of the variables involved. If the result inside the absolute value sign is negative, then removing the absolute value signs will result in its positive counterpart.

Explanation:

When simplifying the expression |ab| given that a<0 and b>0, we consider that since a is negative and b is positive, their product ab will be negative. However, the absolute value signs indicate the positive magnitude of the result, thus |ab| = -ab.

For the expression |2b| where b<0, since b is negative, 2b will also be negative. Removing the absolute value sign should result in a positive number; thus |2b| = -2b.

Lastly, with |c| where c<0, the absolute value of a negative number c is the positive version of the number. Therefore, |c| = -c.

Answer:

The debris will be at a height of 56 ft when time is 0.5 s and 7 s.

Step-by-step explanation:

Given:

Initial speed of debris is, [tex]s=120\ ft/s[/tex]

The height 'h' of the debris above the ground is given as:

[tex]h(t)=-16t^2+120t[/tex]

As per question, [tex]h(t)=56\ ft[/tex]. Therefore,

[tex]56=-16t^2+120t[/tex]

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

[tex]-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0[/tex]

Using quadratic formula to solve for 't', we get:

[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s[/tex]

Therefore, the debris will reach a height of 56 ft twice.

When time [tex]t=0.5\ s[/tex] during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at [tex]t=7\ s[/tex], the height is 56 ft.

Final answer:

To find when the debris will be 56 feet above the ground, we solve the quadratic equation -16t² + 120t = 56 using the quadratic formula. This will yield two possible solutions for t, which are the times at which the debris reaches 56 feet.

Explanation:

To determine when the debris will be 56 feet above the ground, we need to solve the given quadratic equation for t, which represents time in seconds. The equation provided is:

h = -16t² + 120t

Where h is the height in feet. To find the times when the debris is 56 feet above the ground, we set h to 56:

56 = -16t² + 120t

This equation can be solved by factoring or using the quadratic formula. To factor, we first set the equation to zero:

-16t² + 120t - 56 = 0

16t² - 120t + 56 = 0

Dividing by 4

4t² - 30t + 14 = 0

Again reducing by dividing by 2

2t² - 15t + 7 = 0

Now, we need two numbers which add to give 15 and multiply to give 14.

The two numbers are 1 and 14.

2t²- 14t - t + 7 = 0

2t (t - 7) - 1(t - 7) = 0

(t - 7)(2t - 1) = 0

t = 7 or 1/2

Since 1/2 second cannot be an answer, the required answer is 7 seconds

Answer:

yes you can look below for details

Step-by-step explanation:

one reason is because opposite sides are congruent, which means that it is a parallelogram.

another way is to see if the two triangles created by an diagonal is congruent:

construct AC to get two triangles ABC and ADC

AC =CA because of reflection

BA=DC because its given

BC=DA because its also Given

so

triangle ABC= triangle CDA because of SSS(side side side)

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{5}}}\implies \cfrac{-6}{-7}\implies \cfrac{6}{7}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{\cfrac{6}{7}}(x-\stackrel{x_1}{5}) \implies y-3=\cfrac{6}{7}x-\cfrac{30}{7} \\\\\\ y=\cfrac{6}{7}x-\cfrac{30}{7}+3\implies y = \cfrac{6}{7}x+\cfrac{-30+21}{7}\implies y=\cfrac{6}{7}x-\cfrac{9}{7}[/tex]

Answer:

-6/7? I think I'm right but make sure to comment me to let me know!

Step-by-step explanation:

Okay so the equation for slope intercept form is y2-y1/x2-x1. So we can substitute -3-3=-6 and -2-5=-7 So I think you get -6/7

-viridiancat4, an 8th grader

Answer:(i)  84 cm.

(ii)  5635π cm^2

Step-by-step explanation:

(i)

The volume of the cone = 1/3 π r^2 h

= 1/3 π 35^2 h.

The volume of the hemisphere = 2/3 π 35^3.

As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:

1/3 π 35^2 h =  2/3 π 35^3 * 6/5

h =  2/3 π 35^3 * 6/5 /   1/3 π 35^2

h =  84 cm (answer).

(ii)  Surface area of the hemisphere = 2 π * 35^2 =   2450π cm^2.

Surface area of the cone = π r l  where l = slant height.

l = √(35^2 + 84^2) =  91 cm.

So the surface area of the cone =  35*91 π = 3185π.

So the  total surface area of the solid is  3185π + 2450π

= 5635π cm^2.

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Answer:

y = - 4x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Here m = - 4, thus

y = - 4x + b ← is the partial equation

To find b substitute (- 2, 5) into the partial equation

5 = 8 + b ⇒ b = 5 - 8 = - 3

y = - 4x - 3 ← equation of line

Answer:

y= -4x-3

Step-by-step explanation:

to find this, the first step is easy. We know the slope is -4 so we have y= -4x+b. Then we to find the y intersept, so we take the point that we have (-2,5) and make x (the first number) equal to 0. to do this we add two, which means to subtract 8 from give because the slope is -4. This gives the point (0,-3). So the equation is y= -4x-3.

ANSWER:

1/2 (x+3)(x+5)

= 1/2(x^2+8x+15)_This is the right answer

= x^2/2 + 8x/2 + 15/2

= x^2/2 + 4x + 15/2

Mark me as brainst answer

And

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a) The rate of change in this situation is 0.75 dollars/km

b) The equation for the cost of hiring a taxi in terms of length of the

trip is y = 0.75 x + b

c) The initial value represents in this situation is $1.2

Step-by-step explanation:

The given is:

∵ A rate of change is a rate that describes how one quantity

  changes in relation to another quantity

∵ The unit cost of a taxi is 0.75 dollars for each 1 kilometer

∴ The rate of change = 0.75 dollars/km

a) The rate of change in this situation is 0.75 dollars/km

Assume that the cost of hiring a taxi is $y for length of a trip x km

and a base fee of $b

∵ The length of the trip = x km

∵ The cost per km = $0.75

∵ The base fee = $b

∵ The cost of hiring a taxi = $y

- Write an equation for the the cost of hiring a taxi

∴ y = 0.75 x + b

b) The equation for the cost of hiring a taxi in terms of length

of the trip is y = 0.75 x + b

∵ The length of the trip is 10 km

∴ x = 10

∵ The cost of the hiring a taxi is $8.70

∴ y = 8.70

- Substitute these values in the equation of part (b)

∵ y = 0.75 x + b

∴ 8.70 = 0.75(10) + b

∴ 8.70 = 7.5 + b

- Subtract 7.5 from both sides

∴ 1.2 = b

∵ b is the base fee

∴ b is the initial value

∴ The initial value = $1.2

c) The initial value represents in this situation is $1.2

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Answer:

a)  $0.75/Km

b) [tex]F(x)=1.2+0.75x[/tex]

c) The fixed base charge

Step-by-step explanation:

We know the taxi charges $0.75 per km and we are told a 10-Km trip costs $8.70. We can clearly see there is a base charge and a variable charge

a) The rate of change tells us the variation of the charges with the distance of the trip. In this case, the rate of change is $0.75/Km

b) If x is the length of the trip in Km, the equation of the total fare F(x) is

[tex]F(x)=A+0.75x[/tex]

We know a 10-Km trip costs $8.70. Replacing those values would give us the value of A

8.70=A+0.75(10)

8.70=A+7.5

[tex]=> A=8.70-7.5= 1.2[/tex]

Using the value of A we have

[tex]\boxed{F(x)=1.2+0.75x}[/tex]

c) The initial value represents the charge a customer has to pay even if they don't travel any distance, i.e. the fixed base charge

Answer:

40,44,48,52,56,60,64,68...

Step-by-step explanation:

There are 80 birds in the flock of cardinals.

Given:-  A flock of 20 seagulls  or we can say

Number of seagulls in a flock = 20

The new flock is no larger than 100 birds

So, let Total number of birds of new flock = 100

To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.

Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock

Number of birds in cardinal = 100 – 20 =80

Hence there are 80 birds in the flock of cardinals.

The answer explains how to determine the number of birds in the flock of cardinals based on the given conditions.

The number of birds in the flock of cardinals can be calculated as follows:

Let x be the number of birds in the flock of cardinals.

Since the new flock is no larger than 100 birds, the total number of birds after merging is 20 (seagulls) + x (cardinals).

Therefore, the equation to represent this situation is x + 20 ≤ 100, and solving for x, we get x ≤ 80. Thus, there were at most 80 birds in the flock of cardinals.

Answer:

No

Step-by-step explanation:

By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0

f(- 2)

= 2[tex](-2)^{6}[/tex] + [tex]-2)^{5}[/tex] + 32(- 2) + 32

= 2(64) - 32 - 64 + 32

= 128 - 32 - 64 + 32

= 64 ≠ 0

Hence (x + 2) is not a factor of f(x)

Answer: By the factor theorem if (x + 2) is a factor of f(x) then f(- 2) = 0

f(- 2)

= 2(-2)^{6} + -2)^{5} + 32(- 2) + 32

= 2(64) - 32 - 64 + 32

= 128 - 32 - 64 + 32

= 64 ≠ 0

Hence (x + 2) is not a factor of f(x)

Answer:

C is the answer.

Step-by-step explanation: