find the value of the variable and the length of each chord. round your answers to the nearest tenth

Answer: I and III

Step-by-step explanation:

The graphs of f and g have the same axis of symmetry. The graph of f has a maximum point, and the graph of g has a minimum point. The graph is a result of a reflection of the graph pf g across the x-axis. The correct options are 1, 3, and 4.

A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.

We can use the fact that the points (3,2) and (7,2) are on the graphs of both functions to find out which of the given statements are true.

Let's start by using the fact that the graphs of the functions f and g pass through the points (3,2) and (7,2).

Since the y-coordinate is the same for both points, we can set the equations of the functions equal to 2 and solve for the unknown coefficients.

For the downward-opening quadratic function f, the equation is of the form:

[tex]f(x) = a(x - h)^2 + k[/tex]

Where (h,k) is the vertex of the parabola. Since f opens downward, the coefficient a is negative.

Using the point (3,2), we get:

[tex]2 = a(3 - h)^2 + k[/tex]

Using the point (7,2), we get:

[tex]2 = a(7 - h)^2 + k[/tex]

Subtracting the second equation from the first, we get:

[tex]0 = a[(3 - h)^2 - (7 - h)^2][/tex]

Simplifying this expression, we get:

0 = a[(3 - h + 7 - h)(3 - h - (7 - h))]

0 = a[-4(h - 5)]

Since a is non-zero (otherwise the parabola is not quadratic), we get:

h = 5

Plugging in h = 5 and using one of the equations above, we can solve for k:

[tex]2 = a(3 - 5)^2 + k[/tex]

2 = 4a + k

k = 2 - 4a

Therefore, the equation of the quadratic function f is:

[tex]f(x) = a(x - 5)^2 + (2 - 4a)[/tex]

Using the same method for the upward-opening quadratic function g, we get:

[tex]g(x) = b(x - 5)^2 + (2 + 4b)[/tex]

Where b is positive.

Now, let's check which of the given statements are true:

The graphs of f and g have the same axis of symmetry.

Since the vertex of f is (5, 2 - 4a) and the vertex of g is (5, 2 + 4b), the x-coordinate of the axis of symmetry for both functions is 5. Therefore, statement 1 is true.

The graphs of f and g have the same x-intercepts.

The x-intercepts of f are given by:

[tex]0 = a(x - 5)^2 + (2 - 4a)\\4a = a(x - 5)^2[/tex]

x - 5 = ±√(4/a)

x = 5 ± 2√(a)

The x-intercepts of g are given by:

[tex]0 = b(x - 5)^2 + (2 + 4b)[/tex]

-4b = [tex]b(x - 5)^2[/tex]

x - 5 = ±√(-4/b)

x = 5 ± 2i√(b)

Thus, since a and b have opposite signs, the x-intercepts of f and g are different. Therefore, statement 2 is false.

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Answer:

the volume will be 56 m³

because it is made of 56 cubes of 1m ³ volume

I hope it helps

Answer:

1/3 cubic unit

Step-by-step explanation:

Answer:

2m = x

x being the number of tables

Step-by-step explanation:

2 tables = 1 minute

x tables = m

(cross multiply)

2m = x

x being the number of tables

The answer would be A.

Step-by-step explanation:

8 x $2.15= $17.20

Answer:

156 cm

Step-by-step explanation:

Answer:

19 < x < 67

Step-by-step explanation:

triangle inequality theorem:

x + 24 > 43

43 + 24 > x

The range of the possible lengths, in inches, for the third side, x, of this triangle with two sides of a triangle are 24 inches and 43 inches is,

⇒ 19 < x < 67

Any triangle which is a three sided polygon, and, has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The lengths of two sides of a triangle are,

⇒ 24 inches

And,  43 inches.

Hence, The range of the possible lengths, in inches, for the third side, x, of this triangle is find as;

⇒ 43 - 24 < x < 43 + 24

⇒ 19 < x < 67

Therefore, The range of the possible lengths, in inches, for the third side, x, of this triangle with two sides of a triangle are 24 inches and 43 inches is,

⇒ 19 < x < 67

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Answer:

x = 42

Step-by-step explanation:

i hope this helps :)

Answer:

The name of the marked angle is (angle BAD)

Step-by-step explanation:

Answer:

1050 ways

Step-by-step explanation:

Total Number of red balls = 5

Total Number of blue balls = 5

Total Number of white balls = 7

Number of red balls selected = 3

Number of blue balls selected = 4

Number of red balls selected = 5

Using the multiplication and combination relation :

nCr * nCr * nCr

Red balls = 5C3

Blue balls = 5C4

White balls = 7C5

Using calculator:

5C3 * 5C4 * 7C5 = 10 * 5 * 21

(10 * 5 * 21) = 1050 ways

Answer:

The volume of the cylinder is equal to 1205.76 cubic units.

Step-by-step explanation:

Given that,

Height of the cylinder, h = 6

Radius of the cylinder, r = 8

We need to find the volume of the cylinder. The formula for the volume of a cylinder is given by :

[tex]V=\pi r^2 h\\\\V=3.14\times 8^2\times 6\\\\V=1205.76\ units^3[/tex]

So, the volume of the cylinder is equal to 1205.76 cubic units.

Answer:

if we use Pythagorean method, we  could know that A^2+B^2=C^2, so 5^2+12^2 equals 169, and 169 is 13^2

Step-by-step explanation:

Answer:

25 ≤ 2.5n

Step-by-step explanation:

Total budgeted amount = $25

Cost per pack of = $2.50

To represent the relationship using inequality :

Let the Total number of packs purchased = n

Hence,

Total budgeted amount ≤ (cost per pack * number of packs)

25 ≤ 2.5n

This means the total actual purchase made should be less than or equal to the budgeted amount.

Answer:

16

Step-by-step explanation:

Answer:

a) 101°

Step-by-step explanation:

arc HK = 2(39.59°) = 79.18°

arc JH = 180°

arc JK = 360° - 180° - 79.18° = 100.82°

JK = 101°

The correct answer is option (A) 101°

"It is an angle in a circle formed by two chords that have a common end point on the circle."

For given example,

m ∠J = 39.59°

We know, the measure of an inscribed angle in a circle equals half the measure of its intercepted arc.

⇒ m(∠J) = (1/2) × arc KH

⇒ arc KH = 2 × 39.59°

⇒ arc KH = 79.18°

Also, arc HJ = 180°

We know for given figure,

⇒ arc JK + arc KH +arc HJ = 360°

⇒ arc JK + 79.18° + 180° = 360°

⇒ arc JK + 259.18° = 360°

⇒ arc JK = 100.82°

⇒ mJK ≈ 101°

Therefore,  mJK = 101°

The correct answer is option (A) 101°

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Answer:

no

Step-by-step explanation:

Using the converse of Pythagoras' identity

If the square of the longest side is equal to the sum of the squares of the other 2 sides then the triangle is right.

longest side = 17 and 17² = 289

9² + 12² = 81 + 144 = 225 ≠ 289

Then the triangle is not right

Answer:

y + z = x

Step-by-step explanation:

Answer:

Negative

Positive

Negative

Positive

Step-by-step explanation:

AnswerNegative ,Positive, Negative, Positive

Step-by-step explanation:

Answer:

2/36

Step-by-step explanation:

The only outcomes that lead to a sum of 3 are (2,1) and (1,2) therefore there is only a 2 in 36 chance of rolling a sum of 3

Answer:

8x+16

Step-by-step explanation:

i used an app and its never wrong

Answer:

I hate the links too so just look up that exact question and  youll prolly get the right answer

I think the answer it gave was 8

Answer:

9

Step-by-step explanation:

0,1,2

0,2,1

1,2,0

1,0,2

2,0,1

2,1,0

2,2,2

1,1,1

0,0,0

Answer:

A

Step-by-step explanation:

Answer:

1 L = 1000 mL

Step-by-step explanation:

B. 260 × 100

Answer:

C) 10 hours

Step-by-step explanation:

(2.5/200)(800) = 10

Answer:

C

Step-by-step explanation:

i dont really know anything about angles but it looks like the 3x is the exact same angle as 30 degrees on the other side of it

3x=30

x=10

Answer:

YOU DONT KNOW HOW TO ROUND SMH

Step-by-step explanation:

LEARN KID LEARN CMON ITS EASY

Answer:

D. 2/3

If 2/6 equals 1/3, then 1/3 + 1/3 = 2/3.

Answer:

4/6

Step-by-step explanation:

Make 1/3 into 6 as its denominator.

1 x 2 = 2

3 x 2 = 6

Black beans fill up 2/6 of the bag.

Red beans fill up 2/6 of the bag.

Find out what is the fraction both bags fill up altogether.

2/6 + 2/6 = 4/6

Answer:

11^-12 or 11 to the power or negative twelve

Step-by-step explanation:

11^-4  / 11 ^ 8

according to the laws of indices, when dealing with powers, division is subtraction. so:

-4 - 8 = -12

answer = 11^ -12

Answer:

Hello There!

Your answer is:

If this helps, please give me a thanks!!

- abakugosimp

Answer:

Short term Capital gain and $1200

Step-by-step explanation:

Any investment held under a year falls under short term capital gain

5,000 X 0.24 = 1,200

Answer:

Short term Capital gain and $1200.

Step-by-step explanation:

Gains earned by selling assets you’ve held for a year or less are called short-term capital gains, and they generally are taxed at the same rate as your ordinary income, anywhere from 10% to 37%.

Since Rita has a taxable income of $85,000.

So , she fall 24% 82,501 to 157,500 Tax rate bracket.

Therefore     5,000 X 0.24 = 1,200

Thus Rita must pay $1200 in taxes on the Short term Capital gain made by her.

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Answer:

A y C: paralelas

B y A: perpendiculares

B y C: perpendiculares.

Step-by-step explanation:

Sea una recta:

f(x) = a*x + b

Donde a es la pendiente y b es la ordenada al origen.

Otra recta va a ser paralela a esta si tiene la misma pendiente, pero una diferente ordenada al origen, por ejemplo:

g(x) = a*x + c

Y una recta perpendicular a f(x) tendría una pendiente p = -(1/a)

Entonces podemos escribir la línea perpendicular a f(x) como:

h(x) = -(1/a)*x + c

Ahora veamos nuestras líneas:

A(x) =  y = −3*x+5

B(x) = y = x/3+2 = (1/3)*x + 2

C(x) = y = -3*x + 1

Primero veamos cuáles son paralelas:

A(x) y C(x) tienen la misma pendiente (-3) y diferente ordenada al origen, entonces  A y C son paralelas.

Sabiendo que la pendiente de A y C es -3, una línea perpendicular a esta tendría una pendiente:

-(1/-3) = 1/3

Que es justamente la pendiente que tiene la línea B, entonces podemos concluir que B es perpendicular a las líneas A y C.

A y C: paralelas

B y A: perpendiculares

B y C: perpendiculares.