what is the most basic function in a family of the functions?

Answers

Answer 1

Answer:

A family of functions is a group of functions that can all be derived from transforming a single function called the parent function. The parent function is the most basic function in the family of functions, the function from which all the other functions in the family can be derived.A family of functions is a group of functions that can all be derived from transforming a single function called the parent function. The parent function is the most basic function in the family of functions, the function from which all the other functions in the family can be derived.

Step-by-step explanation:

All of the functions within a family of functions can be derived from the parent function by taking the parent function's graph through various transformations.

These transformations include horizontal shifts, stretching or compressing vertically or horizontally, reflecting over the x or y axis, and vertical shifts.

Answer 2

Answer:

The parent function is the most basic.


Related Questions

Find the surface area of a cylinder with a radius 19.3 ft and height 14.7 ft use a calcutor round to the nearest tenth

Answers

To find the surface area of a cylinder, the formula is this:

(2 π r * 14.7ft) + (π r^2 * 2)

So it’s

(2 π 19.3 * 14.7) + (π 19.3^2 * 2) = 4123.0262

Nearest tenth is 4123.0 ft^2

What are the roots of the polynomial ?

Answers

Answer:

B and E

Step-by-step explanation:

By looking at the discriminant, which is [tex]b^2-4ac[/tex], you get that [tex]5^2-4*1*7=25-28=-3[/tex]. Therefore, the only two answers with a -3 inside the square root are B and E.

Answer:

B & E

Step-by-step explanation:

see attached

given sin28.4=.4756, cos28.4=.8796, and tan28.4=.5407 find the cot of 61.6

Answers

Answer:

The cotangent of 61.6° is .5407.

Step-by-step explanation:

Refer to the sketch attached.

61.6° + 28.4° = 90°. In other words, 61.6° is the complementary angle of 28.4°.

Consider a right triangle OAB with a 61.6° angle [tex]\rm O\hat{A}B[/tex]. The other acute angle [tex]\rm O\hat{B}A[/tex] will be 28.4°.

[tex]\displaystyle \tan{61.6\textdegree{}}=\tan{\rm O\hat{A}B} = \frac{\text{Opposite of }\rm O\hat{A}B}{\text{Adjacent of }\rm O\hat{A}B} = \frac{a}{b}[/tex].

The cotangent of an angle is the reciprocal of its tangent.

[tex]\displaystyle \cot{61.6^{\circ}}=\frac{1}{\tan{\rm O\hat{B}A}} = \frac{\text{Adjacent of }\rm O\hat{B}A}{\text{Opposite of }\rm O\hat{B}A} = \frac{a}{b} = \tan{\rm O\hat{A}B} = \tan{28.4^{\circ}}[/tex].

In other words,

[tex]\cot{61.6^{\circ}} = \tan{28.4^{\circ}} \approx 0.5407[/tex].

Factor the trinomial below. x^2-3x-40

Answers

Answer:

(x-8) (x+5)

Step-by-step explanation:

x^2-3x-40

What 2 numbers multiply to -40 and add to -3

-8 *5 = -40

-8+5 = -3

(x-8) (x+5)

Maria practices the piano 5/6 of an hour every day how many hours does she practice in 4 days

Answers

Answer:

20/6 or 3.33 or 3 1/3 or 3 hours and 20 mins

Step-by-step explanation:

5/6 * 4 = (5*4)/6 = 20/6

Answer:

she will have praticed 3 hours and 20 min

Step-by-step explanation:

Find the radius of a circle with the given circumference.
12 x
in.
=
6 inches
6pi
inches
12 inches
24 pi inches

Answers

Answer:

12x=2pi*r

Step-by-step explanation:

2*22/7*r=12x

r=12x*7/44

r=21x/11

The radius of a circle is calculated by dividing the given circumference by 2π. When given circumferences of 6 inches, 6π inches, 12 inches, and 24π inches, the corresponding radii are approximately 0.955 inches, 3 inches, 1.91 inches, and 12 inches, respectively.

To find the radius of a circle given its circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we are given the circumference, we can rearrange this formula to solve for the radius as follows: r = C / (2π).

Given the possible circumferences provided, we can calculate the radius for each.

For 6 inches: r = 6 / (2π) = 6 / (2 * 3.14) = 6 / 6.28 = approximately 0.955 inches

For 6π inches: r = 6π / (2π) = 6 / 2 = 3 inches

For 12 inches: r = 12 / (2π) = 12 / (2 * 3.14) = 12 / 6.28 = approximately 1.91 inches

For 24π inches: r = 24π / (2π) = 24 / 2 = 12 inches

Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)?

f(x) = x + 4
f(x) = x + 6
f(x) = x – 10
f(x) = x – 1

Answers

Answer:

[tex]\large\boxed{f(x)=x+4}[/tex]

Step-by-step explanation:

[tex]y-8=(x-4)\\\\y-8=x-4\qquad\text{add 8 to both sides}\\\\y-8+8=x-4+8\\\\y=x+4\to f(x)=x+4[/tex]

Find the value of x in each of the following exercises:

Answers

Check the picture below.

let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.

[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]

Please explain now thanks

Answers

Answer:

24x - 20

Step-by-step explanation:

4(6x-5)

= 4(6x) - 4(5).............. (Distributive property)

= 24x - 20 (Ans)

Hello There!

The answer would be (24x-20)

We use order of operations so first we would multiply 4 by 6 and get 24x

then, we would multiply 4 by -5 and get -20

Your answer would be 24x - 20

Factor this polynomial completely.
12x^2+ x-6

Answers

Answer:

(3 x - 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + x - 6

Factor the quadratic 12 x^2 + x - 6.

The coefficient of x^2 is 12 and the constant term is -6.

The product of 12 and -6 is -72. The factors of -72 which sum to 1 are -8 and 9.

So 12 x^2 + x - 6 = 12 x^2 + 9 x - 8 x - 6 = 3 (3 x - 2) + 4 x (3 x - 2):

3 (3 x - 2) + 4 x (3 x - 2)

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2):

Answer:  (3 x - 2) (4 x + 3)

The answer is (3 x - 2) (4 x + 3).

Polynomials

Polynomial exists an algebraic expression with terms divided utilizing the operators "+" and "-" in which the exponents of variables exist always nonnegative integers.

Factor the following:

[tex]$$12x^{2}+x-6$$[/tex]

Factor the quadratic

[tex]$12x^{2} +x-6$[/tex]

The coefficient  [tex]x^{2}[/tex] is 12 and the constant term is -6.

The product of 12 and -6 is -72.

The factors of -72 which sum to 1 exist at -8 and 9.

So

[tex]$12 x^{2} +x-6=12 x^{2} +9 x-8 x-6[/tex]

[tex]=3(3 x-2)+4 x(3 x-2)$[/tex]

[tex]$3(3 x-2)+4 x(3 x-2)$[/tex]

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2)

Hence, The answer is (3 x - 2) (4 x + 3).

To learn more about Polynomials refer to:

https://brainly.com/question/13769924

#SPJ2

Solve the given inequality. If necessary, round to four decimal places.


13^4a < 19

Answers

Answer:

The solution of the inequality is a < 0.2870

Step-by-step explanation:

* Lets talk about the exponential function

- the exponential function is f(x) = ab^x , where b is a constant and x

 is a variable

- To solve this equation use ㏒ or ㏑

- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)

* Lets solve the problem

∵ 13^4a < 19

- To solve this inequality insert ㏑ in both sides of inequality

∴ ㏑(13^4a) < ㏑(19)

∵ ㏑(a^n) = n ㏑(a)

∴ 4a ㏑(13) < ㏑(19)

- Divide both sides by ㏑(13)

∴ 4a < ㏑(19)/㏑(13)

- To find the value of a divide both sides by 4

∴ a < [㏑(19)/㏑(13)] ÷ 4

∴ a < 0.2870

* The solution of the inequality is a < 0.2870

Answer:

a < 0.2870

Step-by-step explanation:

We are given the following inequality which we are to solve, rounding it to four decimal places:

[tex] 1 3 ^ { 4 a } < 1 9 [/tex]

To solve this, we will apply the following exponent rule:

[tex] a = b ^ { l o g _ b ( a ) } [/tex]

[tex]19=13^{log_{13}(19)}[/tex]

Changing it back to an inequality:

[tex]13^{4a}<13^{log_{13}(19)}[/tex]

If [tex]a > 1[/tex] then [tex]a^{f(x)}<a^{g(x)}[/tex] is equivalent to [tex]f(x)}< g(x)[/tex].

Here, [tex]a=13[/tex], [tex]f(x)=4a[/tex] and [tex]g(x)= log_{13}(19)[/tex].

[tex]4a<log_{13}(19)[/tex]

[tex]a<\frac{log_{13}(19)}{4}[/tex]

a < 0.2870

what is the measure or angle C?
•25 degrees
•30 degrees
•60 degrees
•75 degrees

Answers

Answer:

25

Step-by-step explanation:

look B=C

so,

A+B+C=180 Sum of all <s of Tri

x+5+3x+3x=180

7x=175

x=175÷7

x=25

Answer: A or 25

Step-by-step explanation:

did the exam on edge 2020

Which of the following is the ratio between the number of successes and the number of possible outcomes of an event?​

Answers

The correct answer is: Probability
probability is your believe it

What is the radius of a circle whose equation is X^2 plus Y^2 -10X +6 X +18=0?

Answers

ANSWER

The radius is 4

EXPLANATION

The given equation is:

[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]

We complete the square to get the expression in standard form:

[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]

[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]

We factor using perfect squares to get:

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]

This implies that,

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]

Comparing to

[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The radius is r=4

NEED HELP ASAP 10 POINT QUESTION

Answers

33,390
You just do

106/100 * 31,500 to find 6% higher

Answer:

The original price of the car can be written in percentage which is 100%. Because the price increased by 6%, therefore, the new price should be represented as:

100% + 6% = 106% = 1.06 (remember: not 0.06, that is how much the price increased, not 0.94 either, because the price increased, not decreased).

So the answer for the first question should be:

(a) new price = 1.06 × original price

from that, we can appy the answer above for the second question:

(b) new price: $33390

25 Points ! Write a paragraph proof.
Given: ∠T and ∠V are right angles.
Prove: ∆TUW ∆VWU

Answers

Answer:

Δ TUW ≅ ΔVWU ⇒ by AAS case

Step-by-step explanation:

* Lets revise the cases of congruent for triangles

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ  

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

 and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

 leg of the 2nd right angle Δ

* Lets solve the problem

- There are two triangles TUW and VWU

- ∠T and ∠V are right angles

- LINE TW is parallel to line VU

∵ TW // VU and UW is a transversal

∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)

- Now we have in the two triangles two pairs of angle equal each

 other and one common side, so we can use the case AAS

- In Δ TUW and ΔVWU

∵ m∠T = m∠V ⇒ given (right angles)

∵ m∠TWU = m∠VUW ⇒ proved

∵ UW = WU ⇒ (common side in the 2 Δ)

∴ Δ TUW ≅ ΔVWU ⇒ by AAS case

Answer:

Step-by-step explanation:

Given ∠T and ∠V are right angles.

TW ║ UV

To prove ⇒ ΔTUW ≅ ΔVWU

Proof ⇒ In ΔTUW and ΔVUW,

∠T ≅ ∠ V ≅ 90° (given)

Side UW ≅ UW ( Common in both the triangles )

TW ║ UV

and UW is a transverse.

So ∠TWU ≅ ∠WUV [alternate interior angles]

Since Angle = Angle = side are equal

Therefore, ΔTUW ≅ ΔVWU

Use the properties of exponents to rewrite the expression
(-5uv)(-5uv)(-5uv)(-5uv)

Answers

[tex]\bf (-5u)(-5u)(-5u)(-5u)\implies (-5u)^1(-5u)^1(-5u)^1(-5u)^1 \\\\\\ (-5u)^{1+1+1+1}\implies (-5u)^4\implies (-5)^4u^4\implies 625u^4[/tex]

Find the value of z.

Answers

Answer:

[tex]\large\boxed{\dfrac{50}{3}}[/tex]

Step-by-step explanation:

If the polygons are similar, then the corresponding sides are in proportion:

[tex]\dfrac{z}{10}=\dfrac{20}{12}[/tex]        cross multiply

[tex]12z=(10)(20)[/tex]

[tex]12z=200[/tex]         divide both sides by 12

[tex]z=\dfrac{200}{12}\\\\z=\dfrac{200:4}{12:4}\\\\z=\dfrac{50}{3}[/tex]

Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5), and point A’ is located at (-2,1). What is the distance from B to B’?

Answers

Answer:

The distance from B to B’ is [tex]5\ units[/tex]

Step-by-step explanation:

we know that

In a translation the shape and dimensions of the figure are not going to change.

therefore

AA'=BB'=CC'=DD'

Find the distance AA'

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex]A(1,5)\\A'(-2.1)[/tex]  

substitute the values

[tex]AA'=\sqrt{(1-5)^{2}+(-2-1)^{2}}[/tex]

[tex]AA'=\sqrt{(-4)^{2}+(-3)^{2}}[/tex]

[tex]AA'=\sqrt{25}[/tex]

[tex]AA'=5\ units[/tex]

therefore

[tex]BB'=5\ units[/tex]

Find the 11th term of this sequence -10, 20, -40

Answers

Answer:

Step-by-step explanation:

the nth term of the geometric sequence  is :  An =A1 × r^(n-1)

A1 = -10

r= -40/20=20/-10=-2

n =11

A11 = -10× (-2)^(11-1)

A11 = -10× (-2)^(10)

A11 = - 10240

Answer:

-10,240.

Step-by-step explanation:

This is a geometric sequence with common ratio 20/-10 = -40/20 = -2.

The nth term = a1r^(n-1)   where a1 = the first term and r = the common ratio, so the 11th term = -10 * (-2)^ (11-1)

= -10 * 1024

= -10,240.

PLEASE someone help me with maths ​

Answers

You are on the right tracks.

Since angle ABC is a right angle, that means lines AB and BC are perpendicular.

Therefore the gradient of BC = the negative reciprocal of the gradient of AB. We can use this to form an equation to find what K is.

You have already worked out the gradient of AB ( 1/2)  (note it's easier to leave it as a fraction)

Now lets get the gradient of BC:

[tex]\frac{5-k}{6-4}= \frac{5-k}{2}[/tex]

Remember: The gradient of BC = the negative reciprocal of the gradient of AB. So:

[tex]\frac{5-k}{2} =negative..reciprocal..of..\frac{1}{2}[/tex]

So:

[tex]\frac{5-k}{2}=-2[/tex]           (Now just solve for k)

[tex]5-k=-4[/tex]

[tex]-k=-9[/tex]                          (now just multiply both sides by -1)

[tex]k = 9[/tex]

That means the coordinates of C are: (4, 9)

We can now use this to work out the gradient of line AC, and thus the equation:

Gradient of AC:

[tex]\frac{1-9}{-2-4} =\frac{-8}{-6} = \frac{4}{3}[/tex]

Now to get the equation of the line, we use the equation:

y - y₁ = m( x - x₁)                            

Let's use the coordinates for A (-2, 1), and substitute them for y₁  and x₁  and lets substitute the gradient in for m:

y - y₁ = m( x - x₁)    

[tex]y - 1=\frac{4}{3}(x +2)[/tex]           (note: x - - 2 = x + 2)

Now lets multiply both sides by 3, to get rid of the fraction:

[tex]3y - 3 = 4(x+2)[/tex]             (now expand the brackets)

[tex]3y - 3 = 4x+8)[/tex]              

Finally, we just rearrange this to get the format: ay + bx = c

[tex]3y - 3 = 4x+8[/tex]              

[tex]3y = 4x+11[/tex]

[tex]3y - 4x = 11[/tex]          

And done!:

________________________________

Answer:

The equation of a line that passes through point A and C is:

[tex]3y - 4x = 11[/tex]        

             

Which point lies on a sphere?
J
B
S

Answers

Is letter B
Because the sphere means the outside part of the sphere, not inside of it

Answer:

Point B lies on a sphere.

Step-by-step explanation:

Remember, a sphere is defined as a three-dimensional object where all points on its surface are equidistant form its center.

According to its definition, all point on the boundaries can be called a point on the sphere.

So, among the options, only point B is on the sphere, because J and S are inside.

Therefore, the right answer is Point B.

Which mapping represent a relation is a function PLEASE HELP ASAP

Answers

Mapping A shows x--->y. A is the answer. Exactly one x value is matched to exactly one y value.

cube root of y equals 4​

Answers

Answer:

y = 64

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\sqrt[3]{y}=4\qquad\text{cube of both sides}\\\\(\sqrt[3]{y})^3=4^3\\\\y=64\\\\\bold{METHOD\ 2:}\\\\\text{Use the de}\text{finition of cube root}:\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\sqrt[3]{y}=4\iff 4^3=y\to y=64[/tex]

Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?

Answers

Answer: [tex]945\ pixels[/tex]

Step-by-step explanation:

We know  that the original photo was 800 pixels wide and the new photo will be 1,260 pixels wide. Therefore,  we can find the scale factor.

Divide the width of the new photo by the width of the original photo. Then the scale factor is:

[tex]scale\ factor=\frac{1,260\ pixels}{800\ pixels}\\\\scale\ factor=\frac{63}{40}[/tex]

The final step is to multiply the height of the original photo by the scale factor calculated.

Therefore the height of the new photo will be:

[tex]h_{new}=(600\ pixels)(\frac{63}{40})\\\\h_{new}=945\ pixels[/tex]

Answer:

945 pixels.

Step-by-step explanation:

Givens

The original photo dimensions are (800 wide x 600 high )pixelsThe new photo is 1,260 pixels wide.

First, we need to find the scale factor by dividing

[tex]s=\frac{1260}{800}=1.575[/tex]

Then, we multiply the height by the scale factor

[tex]600 \times 1.575 = 945[/tex]

Therefore, the new height is 945 pixels.

There are 19 sticks of gum left in one packet, and 6 sticks of gum in another packet that are going to be split evenly between 2 people. How many sticks of gum does each person get? Choose the correct answer from the choices below.

Answers

[tex]19 + 6 = 25 \div 2 = 12.5[/tex]

Answer:

12.5

Step-by-step explanation:

19+6=25 , 25÷2= 12.5

A line goes through the points
(−5,−8)
and
(5,2)
. Find its slope.

Answers

Answer:

Slope is 1

Step-by-step explanation:

Rise over Run.  Delta y over Delta x.  -8-2/-5-5 = -10/-10 = 1

answer

slope is 1
and they are explaining it on top

Can someone help me with this

Answers

Answer:

No, because they look like they are different sizes. Or you could say the first answer

Hello There!

The answer is "C"

In this problem, you need dilation to map onto each-other.

Dilation is transformation hat changes the size of something

The equation below describes a circle. What are the coordinates of the center of the circle? (X-6)^2+(y+5)^2=15^2

Answers

Answer:

Step-by-step explanation:

6,-5 ON APEXXXXX

Answer: (6, -5)

Step-by-step explanation:

The general equation of a circle is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is center and r is radius of the circle.

Given : The equation of a circle : [tex](x-6)^2+(y+5)^2=15^2[/tex]

[tex]\Rightarrow\ (x-6)^2+(y-(-5))^2=15^2[/tex]

Comparing to the general equation of circle , we get

[tex](h,k)=(6, -5)[/tex]

Hence, the coordinates of the center of the circle = (6, -5)

Which expression best estimates 6 3/4 divided by 1 1/2?

Answers

Answer:

7/2

Step-by-step explanation:

Round 6 3/4 to 7

Round 1 1/2 to 2

7 divided by 2

=7/2

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