A number decreased by 25 is equal to 214. Find the number,

We are given with a quadratic equation which represents a Parabola , we need to find the vertex of the parabola , But let's recall that , For any quadratic equation of the form ax² + bx + c = 0 , the vertex of the parabola is given by ;

[tex]{\quad \qquad \boxed{\bf{Vertex = \left(\dfrac{-b}{2a},\dfrac{-D}{4a}\right)}}}[/tex]

Where , D = b² - 4ac (Discriminant)

Now , On comparing the given equation with ax² + bx + c , we have

⇢⇢⇢ a = 1 , b = - 10 , c = 27

Now , Calculating D ;

[tex]{:\implies \quad \sf D=(-10)^{2}-4\times 1\times 27}[/tex]

[tex]{:\implies \quad \sf D=100-108}[/tex]

[tex]{:\implies \quad \bf \therefore \quad D=-8}[/tex]

Now , Calculating the vertex ;

[tex]{:\implies \quad \sf Vertex =\bigg\{\dfrac{-(-10)}{2\times 1},\dfrac{-(-8)}{4\times 1}\bigg\}}[/tex]

[tex]{:\implies \quad \sf Vertex = \left(\dfrac{10}{2},\dfrac{8}{2}\right)}[/tex]

[tex]{:\implies \quad \bf \therefore \quad Vertex = (5,2)}[/tex]

Hence , The vertex of the parabola is at (5,2)

Note :- As the Discriminant < 0 . So , the equation will have imaginary roots .

Refer to the attachment for the graph as well .

Answer:

  390

Step-by-step explanation:

The given sequence has no common difference or ratio, so finding the rule that describes it is mainly accomplished by trial and error.

__

We notice that the ratio of the first two numbers is 2, the difference of the second pair is 3, the ratio of the third pair is 4, the difference of the next pair is 5.

This suggests that we are alternating addition and multiplication, and that the values involved increase by 1 each time.

Addition of 5 was used last, so we expect the next number to be found by multiplying by 6.

  65 × 6 = 390 . . . . . the next number

8:30 as a start time is the most popular time with students because, in sample 1, it has eighteen people supporting it as compared to the other start times which have twelve supporters for 7:45 am start time and ten supporters for 9:00 am start time. In Sample 2, it has nineteen people supporting it as compared to fourteen supporters for 7:45 am start time and seven supporters for 9:00 am start time

Answer:

y = x -3

Step-by-step explanation:

From the graph we see the line goes from point (0, -3) to point ( 3, 0), so we can find the slope as m= rise ( go up 3)  / run ( go to the right 3)  = 3/ 3 = 1

From the graph we can also see the y-intercept ( where the line intersects the y axis is at b = -3

The general equation of the line is y= mx+ b

Our line's equation is y = x -3, because m=1 and b= -3

Answer: a=1 b=3

Step-by-step explanation: the x for each of the points are 1 and 3

A domain is the range of the assigned value (x), the domain of this piecewise-defined function are: a= 1 and b= 3

Based on the graph of the piecewise-defined function, we can deduce the following points;

When x < 1, we have:

f(x) = -x.

When 1 ≤ x < 3, we have:

f(x) = -1.

When x ≥ 3, we have:

f(x) = (x - 3)² - 1.

Since a domain is the range of the assigned value (x), we have:

a = 1.

b = 3.

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Step-by-step explanation:

no

yes

no

no

the sum of all angles must be 180°

Answer:

2

Step-by-step explanation:

Because

2 hours=1 lawn

4 hours=2 lawns

6 hours=3 lawns

8 hours=4 lawns

10 hours=5 lawns

12 hours=6 lawns

14 hours=7 lawns

16 hours=8 lawns

18 hours=9 lawns

Another way to think of it is 18 hours by 9 lawns=2 so each 2 hours the lawns should be half like how 12 hours is 6 lawns or how 16 hour is 8 lawns.

Hope this helps have a great afternoon:)

The rate of mowing the lawn by Meena is 2 units per hour, at this rate she will mown 9 lawns in 18 hours.

Given, that Meena mowed 9 lawns in 18 hours.

The breakup of lawn mowing by Meena can be described as below.

She mowed 9 lawns in 18 hours.

So, the breakup :

2 hours = 1 lawn

4 hours = 2 lawns

6 hours = 3 lawns

8 hours = 4 lawns

10 hours = 5 lawns

12 hours = 6 lawns

14 hours = 7 lawns

16 hours = 8 lawns

18 hours = 9 lawns

In this way she mowed 9 lawns in 18 hours with a rate of 2 lawns per hour.

Know more about per unit rate system,

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Answer:

1. 5 hours

2. 4 hours

Reason:

Formula for speed is speed = [tex]\frac{distance}{time}[/tex] , if you want to find time, then take distance / speed, which will equal to 100 / 20 = 5 hours, and the same with 2.

[tex]\\ \rm\hookrightarrow Speed=\dfrac{Distance}{Time}[/tex]

[tex]\\ \rm\hookrightarrow Time=\dfrac{Distance}{Speed}[/tex]

So

#1

[tex]\\ \rm\hookrightarrow Time=\dfrac{100}{20}=5h[/tex]

#2

[tex]\\ \rm\hookrightarrow Time=\dfrac{180}{45}=4h[/tex]

y = 5x

63.5 = 5x

x = 12.7 hours

The number of hours did Brianna work, if she was paid amount $63.50 as salary, is 12.7 hours.

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation using the variable in place of unknown numbers.

Brianna uses the equation to calculate here pay is,

[tex]y = 5x[/tex]

Here y represents the amount of pay, and x represents the number of hours worked.

The number of hours did Brianna work if she was paid $63.50 has to be find out.

As the total amount, Brianna get is $63.50 and this is represented by the variable y in the above equation.

Thus, put the value of y in the above equation to find the value of number of hours as,

[tex]63.50= 5x\\x=\dfrac{63.50}{5}\\x=12.7[/tex]

Hence, the number of hours did Brianna work, if she was paid amount $63.50 as salary is 12.7 hours.

Learn more about the unknown variable here;

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Answer:

x = 1

Step-by-step explanation:

The standard equation for a inversely proportional relation is:

y = k/x

We can use the given (x, y) point, (3, 80), to find the value of k.

y = k/x

80 = k/3

k = 80 × 3

k = 240

Now we can write the equation using the value we found for k.

The inversely proportional relation is:

y = 240/x

We now let y = 24 and solve for x.

y = 24/x

24 = 24/x

24x = 24

x = 1

Answer: x = 1

Answer:

(3y+2) (2d+9)

Step-by-step explanation:

Group and factor out the greatest common factor then combine.

Answer:

For B.) Estimate how many inches in a triangle, the edges for B.) Estimate it to around 5 or 4 ok and you times the other 4, start from bottom to end. so 4x4x3x3= 144

4x4=16

3x3=9

16x9=144

Step-by-step explanation:

Answer:

Step-by-step explanation:

ABCD is a rectangle

Base = 4 - (-5) = 9

Height = 4 - (-6) = 10

Area = 9 * 10 = 90 ft²

Check the picture below.

Answer:D

Step-by-step explanation: x-coordinate is same ( from picture), but height is different(y)

Answer:

OPTION D.

Step-by-step explanation:

Given:-

An image of house in the graph.

To find which option is correct.

So here we can notice that the roof top and the right side of the door is on a same straight line.

And it lies in the first co-ordinate.

So in the first coordinate in a straight line the value of x is always the same and only the value of y increase or decrease.

So here the correct option is OPTION D.





Answer:

the answer is A

Step-by-step explanation:

angle y=163  and angle x= angle z  

Answer:

-27.27 %

Step-by-step explanation:

((y2 - y1) / y1)*100 = your percentage change

(where y1=start value and y2=end value)

((12 - 16.5) / 16.5) * 100 = -27.27 %

27.3%

Find the different:

16.50-12=4.5

Find the percentage reduction:

4.5/16.50×100

=27.27272727

=27.3%(3 sig.fig)

Answer:

radical form, they occur as two conjugates.

That is,

The conjugate of (a + √b) is (a - √b) and vice versa.

To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.

Answer:

17/8

Step-by-step explanation:

2⅛ as an improper fraction.

2 x 8 = 16

16 + numerator (1) =17.

17/8 is 2⅛ as an improper fraction

Solution:

To convert the fraction into improper fraction, multiply the whole number with the denominator and add the numerator to the product. The denominator will remain the same.

2 1/8 in improper fraction is 17/8.

Answer:

hope it will help you

Answer:

14

Step-by-step explanation:

Answer:

x > 2

Step-by-step explanation:

2(x + 5) < 4 + 5x

expand brackets:

⇒ 2x + 10 < 4 + 5x

Subtract 2x from both sides:

⇒ 10 < 4 + 3x

Subtract 4 from both sides:

⇒ 6 < 3x

⇒ 3x > 6

Divide both sides by 3:

⇒ x > 2

Answer: x>2

Step-by-step explanation: Check the steps in these attached images your welcome.

Simplify the expression

Answer:

203.25 (1 = remainder)

Step-by-step explanation:

Answer:

1. C

2. A

3. B

Step-by-step explanation:

hope it helps you!

Answer:

20 and 20 = vertical angles

20 and 70 = complimentary angles

20 and 160 = supplementary angles

Step-by-step explanation:

vertical angles are the same measure, complimentary angles add up to 90, and supplementary angles add up to 180

Answer:

Step-by-step explanation:

Sarha picker 1/2 more thank Nathen because

Answer:

$56.25

Step-by-step explanation:

25% of Original Price = 25% of $75 = 0.25*75 = 18.75

The discount is $18.75. This is amount you save.

Final Price = (Original Price) - (Discount)

Final Price = (75) - (18.75)

Final Price = 56.25

Answer:

I caulatuated it and it came down to pay of need is $56.25