Does the graph represent a function?

Answer:

f(x)=x²+1

f(f(x))=(x²+1)²+1

=x⁴+1+2x²+1

=x⁴+2x²+2

choose (2)

[tex] \frac{231}{4} [/tex] ✅

Step-by-step explanation:

[tex] \frac{33}{4} \times \frac{21}{3} \\ = \frac{11 \times 21}{4} \\ = \frac{231}{4} [/tex]

Note:-

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

the number can be either 8 or 3.

Step-by-step explanation:

Let's define N as the "number"

We know that when the square of this number is increased by 24:

N^2 + 24

we got eleven times the original number, then:

N^2 + 24 = 11*N

We just need to solve this for N

To do it, we first move all the terms to one side of the equation:

N^2 - 11*N + 24 = 0

Now we can use the Bhaskara's formula for the zeros of a quadratic equation:

for a general quadratic equation:

a*x^2 + b*x + c = 0

the roots or zeros are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

We get then:

[tex]N = \frac{-(-11) \pm \sqrt{(-11)^2 - 4*1*24} }{2*1} = \frac{11 \pm 5}{2}[/tex]

So we have two solutions:

N = (11 + 5)/2 = 16/2 = 8

N = (11 - 5)/2 = 6/2 = 3

So the number can be either 8 or 3.

Answer:

50

Step-by-step explanation:

Substitute.

Answer:

320

Step-by-step explanation:

(6 x 3)² - 2(12) ÷ 6

324 - 24 ÷ 6

324 - 4

= 320

Answer:

isn't it 5?

by counting the lines from C to B

from C to B the length is 5 while the length of D to C is 6

Answer:

Third option is the correct answer

Step-by-step explanation:

Given end points are: [tex] (x_1, \:y_1) \:\&\: (x_2, \:y_2)[/tex]

[tex] \huge\purple {\therefore Midpoint =\bigg(\frac{x_1+x_2}{2},\: \frac{y_1+y_2}{2}\bigg)} [/tex]

Answer:

Step-by-step explanation:

If AB is tangent to the circle, the AB makes a right angle with the radius BC. That means that triangle ABC is a right triangle and we need Pythagorean's Theorem to find the missing side which is the hypotenuse.

[tex]AC^2=AB^2+BC^2[/tex] and filling in:

[tex]AC^2=14^2+9^2[/tex] and

[tex]AC^2=196+81[/tex] and

[tex]AC^2=277[/tex] so

[tex]AC=\sqrt{277}[/tex] ≈ 16.64

AC = 16.64

"It states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency."

From given diagram,

tangent AB = 14 units

radius BC = 9 units

Using tangent theorem,

AB is perpendicular to BC.

This means ΔABC is right triangle with ∠B = 90°

Using Pythagoras theorem,

[tex]AC^2=AB^2+BC^2[/tex]

⇒ [tex]AC^2=14^{2}+9^{2}[/tex]

⇒ [tex]AC^2=196+81[/tex]

⇒ [tex]AC^2=277[/tex]

⇒ [tex]AC=\sqrt{277}[/tex]

⇒ [tex]AC=16.64[/tex]

Therefore, AC = 16.64

Learn more about tangent to the circle here:

https://brainly.com/question/15279341

#SPJ2

Answer:

7/2

Step-by-step explanation:

12 1/4 is equivalent to the improper fraction 49/4.

The square root of 49/4 is 7/2.

The squareroot of [tex]12 \frac14[/tex] is [tex]3 \frac{1}{2} [/tex].

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \sqrt{12 \frac{1}{4} } \\ \\ = \sqrt{ \frac{49}{4} } \\ \\ = \sqrt{ \frac{7 \times 7}{2 \times 2} } \\ \\ = \sqrt{ \frac{( {7})^{2} }{( {2})^{2} } } \\ \\= \frac{7}{2} \\ \\ = 3 \frac{1}{2} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

Step-by-step explanation:

The standard form of an exponential function is

[tex]y=a(b)^x[/tex] where y is the value of the car after x years have gone by, a is the initial value of the car and b is the rate of depreciation. For us, that looks like this:

[tex]y=64000(.18)^{4.5[/tex] where 64000 is the initial value of the car, .18 is the depreciation rate, and 4.5 is 54 months in years. Doing the math on that gives us that the value of the car will be $51,840 4.5 years after it's purchased new.

9514 1404 393

Answer:

  y = 32°

Step-by-step explanation:

Angle y is one of two congruent base angles in the isosceles triangle BCD that has angle B as its third angle:

  2y + 116° = 180° . . . . . . . sum of angles in a triangle

  y + 58° = 90° . . . . . . . . divide by 2

  y = 32° . . . . . . . . . . . . subtract 58°

_____

To those of you copying this answer: the question here asks for angle y. The other variables can be found from ...

  x = 2y = 64° . . . . . . . the arc is twice the measure of the inscribed angle

  z = ∠CBD = 116°

Answer:

14 cm

Step-by-step explanation:

Use the formula for the area of a square, a = s², where s is the side length of the square.

Plug in 196 as the area, then solve for s.

a = s²

196 = s²

14 = s

So, the length of the pathway is 14 cm

Answer:

18 units

Step-by-step explanation:

The base is 7-4 = 3 units

The height is 8 - 2 = 6 units

P = 2(b+h)

P = 2( 3+6)

P = 2(9)

P = 18

Answer:

84

Step-by-step explanation:

only three number are a multiple of 14

14 * 5 = 70

14 * 6 = 84

14 * 7 = 98

neither 70 nor 98 is a multiple of 4

only 84 is a multiple of 4, 7 and 14

Answer:

1/2             9/8

17/12          23/30

81/70         2/3

Step-by-step explanation:

I ordered it the way it appears in the image.

Answer:

I think it´s 2.

Step-by-step explanation:

7(2) = 14

14+5=19

Pretty simple math for me, not sure about you though.

Answer:

x=2

Step-by-step explanation:

since the two angles are equivalent to each other, we also know that the legs of triangle are equal... so we set the legs equal to each other and solve for x...

7x+5=19

subtract five from both sides

7x=14

divide 7 from both sides

x=2

Answer:

84

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

Prim factorize

7 = 7

14 = 7 * 2

28 = 7 * 2 * 2

42 = 7 * 2 * 3

LCM = 7 * 2* 2  * 3 = 84

Answer:

C) [tex]\sqrt{106}[/tex] units

Step-by-step explanation:

The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where [tex]a[/tex] and [tex]b[/tex] are side lengths of a right triangle and [tex]c[/tex] is the hypotenuse, the longest side of the right triangle.

The distance formula is similar to that of the Pythagorean Theorem which is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points that you wish to find the distance between them in an (x,y) coordinate plane.

Here, we are given that [tex](x_1,y_1)[/tex] is [tex]P(-4,-6)[/tex] and [tex](x_2,y_2)[/tex] is [tex]Q(1,3)[/tex]. So, we can use the distance formula as described previously to find the positive distance between the two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{(1-(-4))^2+(3-(-6))^2}[/tex]

[tex]d=\sqrt{(1+4)^2+(3+6)^2}[/tex]

[tex]d=\sqrt{(5)^2+(9)^2}[/tex]

[tex]d=\sqrt{25+81}[/tex]

[tex]d=\sqrt{106}[/tex]

[tex]d \approx 10.295630141[/tex]

Since all of the given answer choices are in radical form, then C is the correct answer. The distance between the two points is [tex]\sqrt{106}[/tex] units.

Answer:

C

Step-by-step explanation:

Multiply the top and bottom, both by sqrtx-sqrt5. This is in order to rationalize the denominators.

You get answer C.

Answer:

18 scoops is the correct answer

Step-by-step explanation:

3/4 can also be written as 6/8 (multiply both 3 and 4 by 2)

and 1 1/2 is actually 3/2 which can be written as 12/8 (multiply both 3 and 2 by 4)

thus total lentils required is 6/8 + 12/8 = 18/8 cups.

with scoop size 1/8 cup you'll need 18 scoops .

Answer:

18 1/8 scoops

Step-by-step explanation:

Soup:

6 scoops from a 1/8 cup can make a 3/4 cup

Salad:

4 scoops from a 1/8 cup can make a 1/2 cup

If 1/8 means one portion is divided into eight portions, then 8 scoops from a 1/8 cup can make 1 cup.

Answer:

250

Step-by-step explanation:

-150 + 400 = 250

Final Score= -150 + 400

= 250 --- (Answer)

Answer:

a) 0.3429 = 34.29% probability there is 1 red ball out of the 2 balls drawn.

b) 0.3715 = 37.15% probability that there is at least 1 red ball out of 2 balls drawn

Step-by-step explanation:

The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

3 + 5 + 7 = 15 balls, which means that [tex]N = 15[/tex]

3 red, which means that [tex]k = 3[/tex]

2 drawn, which means that [tex]n = 2[/tex]

a) Probability there is 1 red ball out of the 2 balls drawn

This is [tex]P(X = 1)[/tex]

So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,15,2,3) = \frac{C_{3,1}*C_{12,1}}{C_{15,2}} = 0.3429[/tex]

0.3429 = 34.29% probability there is 1 red ball out of the 2 balls drawn.

b) Probability there is at least 1 red ball out of 2 balls drawn

This is:

[tex]P(X \geq 1) = P(X = 1) + P(X = 2)[/tex]

So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,15,2,3) = \frac{C_{3,1}*C_{12,1}}{C_{15,2}} = 0.3429[/tex]

[tex]P(X = 2) = h(2,15,2,3) = \frac{C_{3,2}*C_{12,0}}{C_{15,2}} = 0.0286[/tex]

[tex]P(X \geq 1) = P(X = 1) + P(X = 2) = 0.3429 + 0.0286 = 0.3715[/tex]

0.3715 = 37.15% probability that there is at least 1 red ball out of 2 balls drawn

Answer:

52 degrees

Step-by-step explanation:

Answer:

52 degrees sorry if that's wrong

Answer: D) Reflect over x-axis

=======================================================

Explanation:

When we do this type of reflection, a point like (1,2) moves to (1,-2).

As another example, something like (5,-7) moves to (5,7)

The x coordinate stays the same but the y coordinate flips in sign from positive to negative, or vice versa.

We can say that [tex](x,y) \to (x,-y)[/tex] as a general way to represent the transformation. Note how y = f(x), so when we make f(x) negative, then we're really making y negative.

If we apply this transformation to every point on f(x), then it will flip the f(x) curve over the horizontal x axis.

There's an example below in the graph. The point A(2,8) moves to B(2,-8) after applying that reflection rule.

Answer:

2.05 cm

Step-by-step explanation:

3.14× (n+3)²×10 = 800

31.4(n+3)²=800

(n+3)²= 800/31.4

(n+3)²= 25.48

n+3 =√25.48

n+3= 5.05

n = 5.05 -3 = 2.05

so, the radius should be increased :

2.05 cm

Answer: $46,619

»» 288.44 / 0.7%

»› 41,205

»» 45 x 120.33

»» 5,414

A=41,205

A=5,414

A=46,619

[tex]\color{yellow}{}[/tex]

Answer:

The answer would be $46,619

Step-by-step explanation:

Someone already explained it pretty well, goodluck! :)