Which is a solution to (x - 2)(x + 10) = 13?
O x = 3
Ox=8
x = 10
x = 11

Answer:

f(1) = 1

Step-by-step explanation:

A function can have only one value of y for a given value of x.

Thus, if f(1) = 5, we cannot have f(1) = 1.

We can have f(2) =1 and f(5) = 5, because these are values of y for different values of x,

The first diagram below is the graph of a function, because there is only value of y that corresponds to a given value of x.

The second diagram is not the graph of a function, because there are two values of y that correspond to a given value of x.

However, the top semicircle and the bottom semicircle separately are graphs of functions, because they each have only value of y that corresponds to a given value of x.

Final answer:

The statement that could not be true for a function f(x) where f(1) = 5 is any claim that f(x) takes a different value than 5 for any x within the domain [0, 20], where f(x) is described as a horizontal line. Therefore, if f(1) = 5, it must be true that f(x) = 5 for all x in [0, 20].

Explanation:

If f(x) is a function and f(1) = 5, then it indicates that when we input 1 into the function f, we get the output of 5. The question asks which statements could not be true based on this piece of information and additional details regarding the nature of function f. The provided information suggests that the graph of f(x) is horizontal for 0 ≤ x ≤ 20, which means the output value of f(x) is the same for any input value x within that domain.

Likewise, we can determine some possible characteristics of f(x) based on the nature of continuous functions. Adding a constant to f does not affect the derivative, so despite the value of f at x = 1 being 5, we cannot deduce the exact form of f but can infer its behavior around that point. It is essential to note that when a function is defined as a continuous horizontal line within a certain domain, its value is constant across that domain. As a result, if f(1) = 5 for the function f(x) = a horizontal line on the interval [0, 20], it implies that f(x) must be 5 for all x in that interval.

Therefore, any statement that implies the function has a different value than 5 for any x in [0, 20] cannot be true. For instance, if there were a claim that f(2) ≠ 5 or that f(x) is not defined for some x within the interval where it is supposed to be a horizontal line, such a statement would be false given the function's described behavior.

Answer:

Law of Cosines

Angle A = 45°

Angle B = 51°

Angle C = 84°

Step-by-step explanation:

Law of sines is used when we are given

a) two angles and one side or

b) two sides and non-included angle

Law of cosines is used when we are given

a) three sides or

b) two sides and included angle

In the given question we are given three sides so, Law of Cosines will be used to solve the triangle.

Law of Cosines is:

[tex]a^2 = b^2 + c^2 -2bccos A\\b^2 = a^2 + c^2 -2accos B\\c^2 = a^2 + b^2 -2abcosC[/tex]

We will find the three angles A ,B and C of the triangle using above formula.

a= 10, b=11, c=14

Putting values and finding angle A

[tex]a^2 = b^2 + c^2 -2bccos A\\(10)^2 = (11)^2 + (14)^2 -2(11)(14)cosA\\100 = 121 + 196 -308cosA\\100 = 317 -308 cosA\\100-317 = -308cosA\\-217/-308  = cos A\\0.704 = cos A\\=> A = cos ^{-1}(0.704)\\A= 45[/tex]

Now finding angle B

[tex]b^2 = a^2 + c^2 -2ac cos B\\(11)^2 = (10)^2 + (14)^2 - 2(10)(14)cosB\\121 = 100+196 - 280cosB\\121 -296 = -280cosB\\-175/-280 = cosB\\0.625 = cosB\\=> B = cos^{-1} (0.625)\\B = 51[/tex]

Now finding angle C

[tex]c^2 = a^2 + b^2 -2abcosC\\(14)^2 =(10)^2 + (11)^2 -2(10)(11)cosC\\196 = 100+121 -220cosC\\196 -221 = -220cosC\\-25/-220 = cos C\\0.11 = cosC\\=> C = cos^{-1}(0.11)\\C= 84[/tex]

Answer:

Law of Cosines; A ≈ 45.2°, B ≈ 51.3°, C ≈ 83.5°

Step-by-step explanation:

Answer:

33?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$2,615 i did the math

ANSWER

[tex]w = 50.5[/tex]

[tex]l = 88.5[/tex]

EXPLANATION

The basketball court has a rectangular shape.

The perimeter of this court is calculated using the formula

[tex]P=2(l + w)[/tex]

It is given that,the court has a perimeter of 278ft. Let the width of the court be 'w' units, then the length is "w+38"

The perimeter then becomes:

[tex]2(w + 38+ w) = 278[/tex]

[tex]2w + 38= 139[/tex]

[tex]2w = 139 - 38[/tex]

[tex]2w = 101[/tex]

[tex]w = 50.5[/tex]

[tex]l = 50.5 + 38 = 88.5[/tex]

Check

[tex]P = 2(88.5 + 50.5)[/tex]

[tex]P = 2(139) = 278[/tex]

a LINEar function has well, the graph of a straight line, so this isn't that.

is it a relation? well, yes, because the y-value correlates with the x-value, so one depends or relates to the other.

is it a non-linear function?  well, a function has to pass the vertical line test, meaning if we draw vertical lines they must touch the graph only once on their way down.... and in this case it seems they do, so it is non-linear clearly, and it's also a function.

To determine how many pounds of tomatoes can fit into one crate, calculate 2/3 of a pound for 1/4 of the crate, and then multiply by 4. The answer is 2 1/10 pounds.

A vegetable farmer fills 3/4 of a wooden crate with 2/3 of a pound of tomatoes.

Consecutive numbers means numbers one after another. 1 and 2 are consecutive numbers

The answer would be 18 and 19

18 + 19 is 37

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

0.500.

Step-by-step explanation:

f(x) = 1/16 ^ 1/4

Now 16 ^1/4 = ⁴√16

= 2

so f(x) = 1/2

= 0.500.

Answer: Second Option

x < 22.5; Sam has fewer than 22.5 minutes left to finish running

Step-by-step explanation:

We have the following inequality

[tex]10.5 + x < 33[/tex]

Notice that 10.5 is the amount of time in minutes that Samuel has run.

x represents the amount of additional time it will take to finish the race

33 represents the time limit in which you want to finish the race

The we solve the inequality

[tex]10.5 + x < 33[/tex]

Subtract 10.5 on both sides of the inequality

[tex]10.5 -10.5 + x < 33-10.5[/tex]

[tex]x < 33-10.5[/tex]

[tex]x < 22.5[/tex]

This result means that Samuel must finish the race before 22.5 minutes have elapsed

The answer is the second option

Answer:

X<22.5;sam has fewer than 22.5 left to finish running

Step-by-step explanation:

edgen.

Answer:

36° and 54°

Step-by-step explanation:

We are given that one of the small angles of a right angled triangle is 18 less than twice the measure of the other small angle.

We are to find the measure of both angles.

Assuming [tex]x[/tex] to be the other small angle, 8 less than twice the measure of the other small angle = [tex]2x-18[/tex].

Summing all three angles up ti get:

[tex]x+(2x-18)+90=180[/tex]

[tex]3x=180-90+18[/tex]

[tex]3x=108[/tex]

[tex]x=\frac{108}{3}[/tex]

x = 36°

So other angle will be [tex]2(36)-18=[/tex] 54°.

Answer:

36° and 54°

Step-by-step explanation:

let x be one of the smaller angles, then the other smaller angle is 2x - 18 ( 18 less than twice the other )

Since it is a right triangle then the sum of the 2 smaller angles equals 90, so

x + 2x - 18 = 90

3x - 18 = 90 ( add 18 to both sides )

3x = 108 ( divide both sides by 3 )

x = 36

One angle = 36°

the other angle = (2 × 36) - 18 = 72 = 18 = 54°

Answer:

73.5

Step-by-step explanation:

Put them in order from greatest to least [or vice versa], find the TWO midst quantities, since we are dealing with an EVEN NUMBER of quantities, then you add & divide [in this order] them by 2⃣, since there are TWO midst quantities.

[tex]\bf \cfrac{\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}{\underset{4}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\times \cfrac{\stackrel{1}{\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies \cfrac{1}{4}[/tex]

We are given:

2x + 5 - 3x = 8(x + 1)

We can start with several things. First, we can combine the x terms on the left side of the equation, and apply the distributive property on the right side of the equation.

5 - x = 8x + 8

Now, we can add x to both sides, and subtract 8 from both sides to isolate the variable.

5 - x = 8x + 8

-8 + x  + x -8

We end up with:

9x = -3

By dividing both sides by 9, we get x = [tex]-\frac{1}{3}[/tex].

If you want to check your answer, just plug x in!

2([tex]-\frac{1}{3}[/tex]) + 5 - 3([tex]-\frac{1}{3}[/tex]) = 8([tex]-\frac{1}{3}[/tex] + 1)

[tex]-\frac{2}{3}[/tex] + 5 + 1 = [tex]-\frac{8}{3}[/tex] + 8

[tex]-\frac{2}{3}[/tex] + [tex]\frac{18}{3}[/tex] = [tex]-\frac{8}{3}[/tex] + [tex]\frac{24}{3}[/tex]

[tex]\frac{16}{3}[/tex] = [tex]\frac{16}{3}[/tex]

As you can see, [tex]\frac{16}{3}[/tex] = [tex]\frac{16}{3}[/tex] as a result of having x = [tex]-\frac{1}{3}[/tex].

First you must distribute the 8 to the numbers inside the parentheses

2x + 5 - 3x = 8 (x + 1)

2x + 5 - 3x = 8*x + 1*8

2x + 5 - 3x = 8x + 8

Now you must combine like terms (let's first start with the like terms on the left side). This means the numbers with the same variables must be combined...

-3x + 2x = -x

so...

-x + 5 = 8x + 8

Now you must combine like terms by combining -x with 8x. To do this first add 1x to both sides (what you do on one side you must do to the other). Since x is negative on the left side, addition (the opposite of subtraction/negative) will cancel it out (make it zero) from the left side and bring it over to the right side.

-x + x + 5 = 8x + x + 8

0 + 5 = 9x + 8

5 = 9x + 8

Now bring 8 to the left side by subtracting 8 to both sides (what you do on one side you must do to the other). Since 8 is being added on the right side, subtraction (the opposite of addition) will cancel it out (make it zero) from the right side and bring it over to the left side.

5 - 8 = 9x + 8 - 8

-3 = 9x

Next divide 9 to both sides to finish isolating x. Since 9 is being multiplied by x, division (the opposite of multiplication) will cancel 9 out (in this case it will make 9 one) from the right side and bring it over to the left side.

-3/9 = 9x/9

x = [tex]\frac{-1}{3}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

If the functions f(x) = 7 + 4x and g(x) =1/2x then the value of  (f/g)(5) is 270, option D is correct.

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x) = 7 + 4x and g(x) =1/2x

We have to find the value of (f/g)(5)

We know that from properties of functions

(f/g)(a)=f(a)/g(a)

So let us find f(5) and g(5)

f(5)=27

g(5)=1/10

(f/g)(5)=27/(1/10)

=27×10

=270

Hence, if the functions f(x) = 7 + 4x and g(x) =1/2x then the value of  (f/g)(5) is 270, option D is correct.

To learn more on Functions click:

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Answer:

5

Step-by-step explanation:

Answer:

the answer is five

Step-by-step explanation:

because

Answer:

C. Third option

Step-by-step explanation:

C is the correct answer, because linear function describes a function in which the y values form a geometric sequence.

Hope this helps!

Answer:

y = -20

Step-by-step explanation:

5 + y = -15

Subtract 5 from both sides to isolate y.

y = -15 - 5

y = -20

Hello!

Answer:

[tex]\boxed{y=-20}\checkmark[/tex]

The answer should have a negative sign.

Step-by-step explanation:

First, you switch sides.

[tex]y+5=-15[/tex]

Then, you subtract by 5 both sides.

[tex]y+5-5=-15-5[/tex]

Finally, you simplify.

[tex]-15-5=-20[/tex]

[tex]y=-20[/tex], which is our answer.

Hope this helps!

Thanks!

Have a nice day! :)

-Charlie

Answer:

[tex]A=(9/64)\pi\ units^{2}[/tex]

Step-by-step explanation:

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=(3/4)/2=3/8\ units[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (3/8)^{2}[/tex]

[tex]A=(9/64)\pi\ units^{2}[/tex]

Answer:

Each face of an octahedron is an equilateral triangle. An octahedron is a three-dimensional solid (polyhedron) that has eight faces.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

A) No B) The relation f(8) C) x = 3

Step-by-step explanation:

A) In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.

B) Lets name the upper table outputs "g(x)", so

[tex]g(8) = 8 \: \: and \: \: f(8) = 8 \times 8 - 5 = 64 - 5 = 59[/tex]

[tex]\: 59 > 8 \: \: therefore \: \: f(8) > g(8)[/tex]

C)

[tex]f(x) = 19 \: \: and \: \: f(x) = 8x - 5 \\ 8x - 5 = 19 \\ 8x = 19 + 5 \\ 8x = 24 \\ x = 24 \div 8 \\ x = 3[/tex]

Answer:

The area of the house is approximately 309.54 feet²

Step-by-step explanation:

* Lets describe the figure

- It has a quarter circle with radius = the width of the rectangle

- It has a rectangle with length = 26 - the length of the radius, and

 width 10 feet

- It has a triangle with base equal the length of the rectangle and

 height 8 feet

- It has a trapezoid, the length of its two parallel bases are 2 , 5 and

 height 2 feet

* Lets revise the area of all the shape above

- Area the quarter circle = 1/4 π r²

- Area of the rectangle = length × width

- Area of the triangle = 1/2 × base × height

- Area of the trapezoid = 1/2( the sum of the parallel bases) × height

* Now lets solve the problem

# Area of the quarter circle

∵ The radius of the circle = the width of the rectangle

∵ The width of the rectangle = 10 feet

∴ The radius of the circle = 10 feet

∵ The area of the quarter circle = 1/4 π r²

∴ Its area = 1/4 π (10)² = 25π feet²

# Area of the rectangle

∵ The length of the rectangle = 26 - the length of the radius

∵ the length of the radius = 10 feet

∴ The length of the rectangle = 26 - 10 = 16 feet

∵ The width of the rectangle = 10 feet

∵ The area of the rectangle = length × width

∴ Its area = 16 × 10 = 160 feet²

# Area of the triangle

∵ The base = the length of the rectangle

∵ The length of the rectangle = 16 feet

∴ The base = 16 feet

∵ The height = 8 feet

∵ The area of the triangle = 1/2 × base × height

∴ Its area = 1/2 × 16 × 8 = 64 feet²

# Area of the trapezoid

∵ The length of its two parallel bases are 2 feet , 5 feet

∵ The height = 2 feet

∵ The area = 1/2( the sum of the parallel bases) × height

∴ Its area = 1/2 (2 + 5) × 2 = 7 feet²

- Lets add all of these areas to find the area of the house

∴ The area of the house = 25π + 160 + 64 + 7 = 309.5398 feet²

* The area of the house is approximately 309.54 feet²

Answer:

d. directrix​

Step-by-step explanation:

The name of the green line located below the parabola is directrix​.

Hope this helps! Please mark brainliest!

The point stands named the focus of the parabola and the line exists named the directrix.

A parabola exists a plane curve with a U shape which exists mirror-symmetrical.

The directrix exists perpendicular to the axis of symmetry of a parabola and does not feel the parabola. The line (or "axis") of symmetry exists as the y-axis, even comprehended as the line x = 0. This line stands marked green in the picture. The graph exists said to be "symmetric about the y-axis", and this line of symmetry exists even called the "axis of symmetry" for the parabola.

A parabola exists as a set of all points in a plane that exist an equivalent distance away from a given point and given line. The point stands named the focus of the parabola and the line exists named the directrix.

Therefore, the correct answer is option d. directrix​.

To learn more parabola

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[tex]4\cdot3\cdot2=24[/tex]

Answer:

11.59 units²

Step-by-step explanation:

Step 1 : Determine radius

From reading the graph, looks like the radius is approx 3.2 units

Alternatively,  calculate the radius:

the height of the triangle AOB = 1 unit, 1/2 base of triangle AOB = 3 units.

Using Pythagorean theorem, hypotenuse OB of a right angle triangle,

= √(1² + 3²) = √10 = 3.16 (pretty close to our estimate above)

Area of major sector,

= [tex]\frac{210}{360}[/tex] * area of full circle

= [tex]\frac{210}{360}[/tex] * 2πr

= [tex]\frac{210}{360}[/tex] * 2π (3.16)

= 11.59 units²

Answer:

Step-by-step explanation:

^3√x is improperly formed.  I'd guess you meant "the third root of x," which looks like ∛x.  Note that Brainly's workspace has built-in math symbols.  Try them out by clicking on the Greek letter omega (below).

The domain of f(x) = ∛x is "all real numbers."

Answer:

the domain is the "All real numbers"

First option is correct.

Step-by-step explanation:

We have been given the function [tex]f(x)=\sqrt[3]{x}[/tex]

Domain is the set of x values for which the function is defined.

Here, for the given function, we can take any x values. For each real values of x, the cube root function is defined.

Therefore, the domain is the "All real numbers"

First option is correct.

For this case we have a function of the form [tex]y = f (x)[/tex], where:

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

We must evaluate the function for [tex]x = -3[/tex]

Then we have to replace:

[tex]f (-3) = - (- 3) ^ 2 + 1\\f (-3) = - 9 + 1[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]f (-3) = - 8[/tex]

ANswer:

[tex]f (-3) = - 8[/tex]

The correct answer would be C. 2x^2+7x-4. Hope this helps! :)