the vertex form of a function is g(x)=(x-3)^2+9

Answer:

y = 3

Step-by-step explanation:

*As seen in the photo, the fact that EF = GF and the bisector being there makes EH = HG.

5y + 10 = 28 - y

*Add y to both sides.

6y + 10 = 28

*Subtract 10 from both sides.

6y = 18

*Divide both sides by 6.

y = 3

In triangle EFG, with angle bisector FH and equal lengths for EF and GF, the value of y is 3.

Use the concept of a triangle defined as:

A triangle is a 3-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

Given that,

Angle EFG has an angle bisector FH.

EF = GF (the lengths of the corresponding sides of triangle EFG are equal).

EH = 5y + 10 (length of segment EH).

HG = 28 - y (length of segment HG).

To find the value of y,

Start by applying the angle bisector theorem in triangle EFG.

According to the theorem,

The ratio of the lengths of the segments formed by the angle bisector to the corresponding sides should be equal.

Since EF = GF,

Set up the following equation:

EH / HG = EF / FG

Substituting the given values, we have:

[tex]\dfrac{(5y + 10)}{ (28 - y)} = \dfrac{1} { 1}[/tex]

Cross-multiplying, we get:

5y + 10 = 28 - y

Combining like terms, we have:

6y = 18

Dividing both sides by 6, we find:

y = 3

Therefore, the value of y is 3.

To learn more about the triangle visit;

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Answer:

78.5714

Step-by-step explanation:

given,

radius=5cm

now,

area of circle (A)=

[tex] = \frac{22}{7} \times {5}^{2} \\ \\ \\ = \frac{22}{7} \times 25 \\ \\ = 78.5714 {cm}^{2} [/tex]

Answer:

a=3

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2+4^2 = 5^2

a^2 +16 = 25

a^2 =25-16

a^2 = 9

Taking the square root of each side

sqrt(a^2) = sqrt(9)

a =3

Answer:

Step-by-step explanation:

2x-25,6=90

2x=90+25,6

2x=115,6

x=57,8

Answer:

The number is 57.8

Step-by-step explanation:

Let x = number

2x -25.6 = 90

Add 25.6 to each side

2x-25.6 +25.6 = 90+25.6

2x=115.6

Divide by 2

2x/2 =115.6/2

x =57.8

Answer:

x = [tex]\frac{29}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3}{5}[/tex] = [tex]\frac{x-1}{8}[/tex] ( cross- multiply )

5(x - 1) = 24 ← distribute parenthesis on left side

5x - 5 = 24 ( add 5 to both sides )

5x = 29 ( divide both sides by 5 )

x = [tex]\frac{29}{5}[/tex]

Answer:

see below

Step-by-step explanation:

The domain is the values that the input takes

The values go from 0 to 7

0≤x≤7

This is the time from the initial launch until the object hits the ground

Answer:

the amount he borrowed from b is 540

Answer:

A) He used an incorrect time ratio converting hours to minutes.

D) He incorrectly concluded that she is not running fast enough.

Step-by-step explanation:

Got it right on Edge ✿♥‿♥✿

Answer:

Step-by-step explanation:

a.He used an incorrect time ratio converting hours to minutes.

d.He incorrectly concluded that she is not running fast enough.

Answer:

the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h

Step-by-step explanation:

Let V be the speed of the plane and v the speed of the wind. Down current, they are in opposite directions, and the plane travels a a distance of 4000 km in 5 hours,so

5(V - v) = 4000

V - v = 800    (1)

For upwind movement, since the plane travels 3000 km in 5 hours, so

5(V + v) = 3000

V + v = 600 (2)

adding equations (1) and (2), we have

V - v = 800

+

V + v = 600

2V = 1400

V = 1400/2 = 700 km/h

subtracting equations (2) from (1), we have

V - v = 800

-

V + v = 600

-2v = 200

v = -200/2 = -100 km/h

So, the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h

Answer:

C

Step-by-step explanation:

There are two corresponding angles shown and one included angle meaning the angle is in-between the two sides, allowing this to be characterized by SAS similarity.

Answer:

x = 18

y = 9

y = 9√3/√3 = 9

x = 9×2 = 18

18 people is 25% less people so will take 25% longer

25% of 15 is 3.75

3.75+ 15 = 18.75 days ?

Answer:

-16

Step-by-step explanation:

We are given the expression:

-c+6x

and asked to evaluate when c=4 and x=-2. Therefore, we must substitute 4 in for c and -2 in for x.

-(4)+6(-2)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, Subtraction.

First, multiply 6 and -2.

6 * -2= -12

-(4)+ -12

-(4) -12

Distribute the negative sign.

-4 -12

Subtract 12 from -4.

-16

The expression -c+6x when c=4 and x= -2 is -16.

Answer:

-16

Step-by-step explanation:

Start with -C+ 6x.  Replace C with '4' and x with '-2'

This comes out to -(4) + 6(-2) = -4 - 12 = - 16

Answer:

4 x 3

Step-by-step explanation:

The order of a matrix is given by stating the number of rows followed by the number of columns.

The matrix here has 4 rows and 3 columns thus order is

4 x 3

Answer:

Movement along the demand curve

Step-by-step explanation:

edge 2021.

The change in price as shown in the graph is shown as movement along the demand curve.

The terms demand and supply are common themes in economics. They show the relationship between the amount that a seller wants to sell and the amount that a buyer wants to buy. A number of factors affect the demand curve.

The change in price as shown in the graph is shown as movement along the demand curve.

Learn more about demand and supply: https://brainly.com/question/13353440

Answer:

The measure of angle B is 54°. The measure of angle A is 51°. The measure of angle AFE is 47°.

Answer:

288*pi

Step-by-step explanation:

Area=2*pi*(24)^2*(90/360)=288*pi

Answer:

convert into a whole number 6

Answer:

99

Step-by-step explanation:

x = 90 x 10/100 + 90

=> x = 900/100 + 90

=> x = 9 + 90

=> x = 99

Answer:

9,580,000

Step-by-step explanation:

The ten thousand place is the 8

look and the thousands place which is 3

This is less than 5 so we leave the ten thousands place alone

9,583,507 becomes

9,580,000

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{9,583,507}[/tex]

[tex]\huge\textsf{= 9,600,000} \leftarrow \huge\textsf{nearest \underline{\underline{HUNDRED}} thousand}[/tex]

[tex]\huge\textsf{= 9,580,000} \leftarrow\huge\textsf{nearest \underline{\underline{TEN}} thousand}[/tex]

[tex]\large\textsf{83 is rounded to 80 because it is closer to 80 than 90. 3 is closer to}\\\large\textsf{0 than 10}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 9,580,000}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day! }[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

43/90

Step-by-step explanation:

We want to express 0.47777... as a ratio of two integers. To do so, we need to multiply by 10^n, where n is the number of repeating decimals. Only 7 is repeating so we multiply 0.47777... by 10. The trick to do this is to let x=0.47777... In other words, what we are doing is the following:

[tex]x=0.47777...\\10x=4.7777....\\\text{Subtract x}\\10x-x=4.7777...-x\\9x=4.7777...-0.4777...\\9x=4.3\\x=4.3/9=43/90=0.4\overline{7}[/tex]

Answer:

x=6

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x-(24)=0

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  4x - 24  =   4 • (x - 6)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true

2.1      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    x-6 = 0

Add  6  to both sides of the equation :

                     x = 6

One solution was found :

x = 6

Answer:

x= 24/ 4

Step-by-step explanation:

You can simplify it

x= 6/1 which is x= 6

Answer:

we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10

Step-by-step explanation:

From the given information;

Sample  size n = 12

the probability of passing a student who guesses on every question is less than 0.10

In a alternative - response question (true/false) question, the probability of answering  a question correctly  = 1/2 = 0.5

Let X be the random variable that is represent number of correct answers out of 12.

The X [tex]\sim[/tex] BInomial (12, 0.5)

The probability mass function :

[tex]P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}[/tex]

[tex]P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}[/tex]

P(X = 12) = 2.44 × 10⁻⁴

[tex]P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}[/tex]

P(X =11 ) = 0.00293

[tex]P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}[/tex]

P(X = 10) = 0.01611

[tex]P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}[/tex]

P(X = 9) = 0.0537

[tex]P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}[/tex]

P(X = 8)  = 0.12085

[tex]P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}[/tex]

P(X = 7) = 0.19335

.........

We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01

As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10

Answer:

< UTS = 129

Step-by-step explanation:

< UTS= <CTS+ < UTC

x + 129 = 105+  2x + 24

Combine like terms

x+129=2x+129

Subtract x from each side

129 +x-x = 2x-x+129

129 = x+129

Subtract 129 from each side

129-129 = x+129-129

0 =x

< UTS =  x + 129  = 0+129 =129

Answer:

[tex]y=-(x-3)^2+1[/tex]

Step-by-step explanation:

Hi there!

Vertex form: [tex]y=a(x-h)^2+k[/tex] where [tex]a[/tex] is a scale factor and [tex](h,k)[/tex] is the vertex of the parabola

On the graph, we can determine that the vertex of this parabola is (3,1). Plug this into [tex]y=a(x-h)^2+k[/tex]:

[tex]y=a(x-3)^2+1[/tex]

The value of a must either be -1 or 1 because the graph has not been stretched or compressed vertically. How can we tell? Well, starting from the vertex, if we increase x by 1, y only changes by 1. If we decrease x by 1 starting from the vertex, y only changes by 1. This wouldn't be the case if the graph had been stretched or compressed.

Now, because this is a downward-facing parabola, we know that the value of a is negative. Because a can only be -1 or 1, a is therefore -1. Plug this into [tex]y=a(x-3)^2+1[/tex]:

[tex]y=-(x-3)^2+1[/tex]

I hope this helps!

Answer:

Below

Step-by-step explanation:

● vector ED:

Vector ED = a since the Vectors ED and AB are colinear and have the same sense.

● vector CD:

Vector CD = -b since the vectors FA and CD are colinear but have opposite senses.

● Vector FB:

Vector FB = a+b

Using Chasles relation, we can express FB as the sum of the Vectors FA and AB.

● Vector BE:

Vector BE= -2b

The vectors BE and FA are colinear but have different senses. BE has a magnitude that is the double of FA's one.

●Vector EF:

Again using Chasles, relation we can express EF as the sum of the vectors FA and AB.

Vector EF= a+b

● Vector CF:

Vectors CF and AB are colinear but have opposite senses. The distance CF is the double of AB.

So: Vector CF=a+b

Answer:

x = 12

Step-by-step explanation:

The sum of the two smaller angles is 140

80+5x = 140

Subtract 80 from each side

80+5x-80 =140-80

5x = 60

Divide each side by 5

5x/5 = 60/5

x = 12

Answer:

This is because there are equal counts of both even and odd numbers

Step-by-step explanation:

Here in this question, we are concerned with stating the reason why it is likely that a standard number cube have the same probability for showing an even number as well as an odd number.

In the number cube, the odd numbers are 1,3 and 5. While the even numbers are 2,4 and 6.

From here, we can see that there are three set of each number types. What this automatically means is that the probability of selecting an even number will be equal to the probability of selecting an odd number. Thus, we can say that it is just as likely that the cube will show an even number as an odd number because each of the type of numbers have 3 values each.

Answer:

[tex]\boxed{A. (1,1)}[/tex]

Step-by-step explanation:

Well since in,

[tex]f(x) = -3x^2 + 6x - 2[/tex]

the 3x^2is negative that means the parabola has a maximum not a minimum meaning we can take out choices,

B and D.

To find the maximum let’s graph the given equation,

Look at the image below.

By looking at the image we can tell that the maximum is at (1,1).

So the answer is choice A (1,1)