Suppose $f(3) = 4$. Name a point that must be on the graph of $y=f(x)+4.$

Enter your answer as an ordered pair.

Answer:

Minimum

Step-by-step explanation:

The zeros of a quadratic equation are the points at which the parabola intersects the x-axis.

[tex]\sf x=3 \implies x-3=0[/tex]

[tex]\sf x=7 \implies x-7=0[/tex]

[tex]\sf \implies y=a(x-3)(x-7)[/tex]   (for some constant a)

[tex]\sf \implies y=ax^2-10ax+21a[/tex]

The optimal value is the y-coordinate of the vertex.  

[tex]\sf \implies vertex=(x,-3)[/tex]

The x-coordinate of the vertex is the midpoint of the zeros:

[tex]\sf x=\dfrac{7-3}{2}+3=5[/tex]

[tex]\sf \implies vertex=(5,-3)[/tex]

Therefore, the vertex will be in Quadrant IV and so the parabola opens upwards into Quadrant I.  

So the optimal value is a MINIMUM since the vertex is the minimum point of the curve.

Additional Information to create the equation of the quadratic

Vertex form of quadratic equation:  [tex]\sf y=a(x-h)^2+k[/tex]

where (h, k) is the vertex

[tex]\sf \implies y=a(x-5)^2-3[/tex]

[tex]\sf \implies y=ax^2-10ax+25a-3[/tex]

To find the value of a, compare the constants of both equations:

[tex]\sf 21a=25a-3[/tex]

[tex]\sf \implies -4a=-3[/tex]

[tex]\sf \implies a=\dfrac34[/tex]

So the final equation is:

[tex]\sf factor \ form \implies y=\dfrac34(x-3)(x-7)[/tex]

[tex]\sf standard \ form\implies y=\dfrac34x^2-\dfrac{15}{2}x+\dfrac{63}{4}[/tex]

[tex]\sf vertex \ form \implies y=\dfrac34(x-5)^2-3[/tex]

it goes through the point (2, 10), has a vertex at (5, 1) and goes through the point (8, 10)

Answer:

Jenna's line would be: C Line L

Step-by-step explanation:

The x coordinates and y coordinates from Jenna's table matches up with the points on Line L. Hope this helped! :)

Answer:

See below ↓↓↓↓↓↓

Step-by-step explanation:

5.

6.

7.

8.

9.

10.

Answer:

12/13

Step-by-step explanation:

P(not a queen) = 48/52 = 12/13

Answer:

48/52

Step-by-step explanation:

Out of a 52 card deck there are 4 queens

there is  a 48/52 propability you will not be drawn a queen or 92.31% you will not be drawn a queen

Answer:

see explanation

Step-by-step explanation:

the area (A) of a trpezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

b₁, b₂ are the parallel bases and h the perpendicular height between them

(1)

b₁ = 12, b₂ = 8 , h = 5

A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 8) = 2.5 × 20 = 50 cm²

(2)

b₁ = 6 , b₂ = 4 , h = 3

A = [tex]\frac{1}{2}[/tex] × 3 × (6 + 4) = 1.5 × 10 = 15 cm²

(3)

b₁ = 7 , b₂ = 4 , h = 4

A = [tex]\frac{1}{2}[/tex] × 4 × (7 + 4) = 2 × 11 = 22 cm²

Answer:

see explanation

Step-by-step explanation:

the area (A) of a trpezoid is calculated as

A = \frac{1}{2}21 h (b₁ + b₂ )

b₁, b₂ are the parallel bases and h the perpendicular height between them

(1)

b₁ = 12, b₂ = 8 , h = 5

A = \frac{1}{2}21 × 5 × (12 + 8) = 2.5 × 20 = 50 cm²

(2)

Answer:

Width = 10 inches

Step-by-step explanation:

A cube is a six-sided shape where each side consists of a square. Since the length of a square is the same measure of the width, then the cube will "work the same way", and the length, width, and height of the cube will all be the same length.

[tex]\sf\large\underline{\star Given:-}[/tex]

[tex]\rightarrow[/tex] Length of rectangular prism = [tex]\sf\red{4m}[/tex]

[tex]\rightarrow[/tex] Width of rectangular prism = [tex]\sf\red{7m}[/tex]

[tex]\rightarrow[/tex] Height of rectangular prism = [tex]\sf\red{8.5m}[/tex]

[tex]\sf\large\underline{\star To \: Find:-}[/tex]

[tex]\sf\large\underline{\star Solution:-}[/tex]

[tex]\rightarrow[/tex] We can find the volume of given rectangular prism by using the formula:

[tex]\sf\blue{Length × Width ×Height}[/tex]

So, let's begin:

[tex]\rightarrow[/tex] Volume of rectangular prism = [tex]\sf{Length × Width ×Height}[/tex](putting the value of length, width and height from the above given)

[tex]\rightarrow[/tex][tex]\sf{=\:4× 7 ×8.5}[/tex]

[tex]\rightarrow[/tex][tex]\sf{=\:28×8.5}[/tex]

[tex]\rightarrow[/tex][tex]\sf{=\:238m^3}[/tex]

Therefore, volume of the given rectangular prism = [tex]\sf\purple{238m^3.}[/tex]

______________________________

Hope it helps you:)

Answer:

statements 2 & 5 are true

Step-by-step explanation:

1. False because is a quadratic nonlinear equation

2. True, 4 is the ordered to the origin

3. False, the rate not being linear is not constant

4. False, because when the input is -3 the output is 13

         [tex]y = (-3)^{2} +4=9+4=13[/tex]

5. True, y depends on x

Hope this helps

Answer:

Eleanor has made an error in Step 1

She clearly intended to multiply both sides by 2, but forgot to multiply the [tex]-9x[/tex] part of the RHS.

Step 1 should be:   [tex]x+18=8(2x-6)-18x[/tex]

Correct solution

Given:   [tex]\dfrac12(x+18)=4(2x-6)-9x[/tex]

Step 1:  [tex]x+18=8(2x-6)-18x[/tex]

Step 2:  [tex]x+18=16x-48-18x[/tex]

Step 3:  [tex]x+18=-48-2x[/tex]

Step 4:  [tex]66=-3x[/tex]

Step 5:  [tex]x=-22[/tex]

Answer: 907.46

Step-by-step explanation:

Answer:

4 and 9

Step-by-step explanation:

Composite numbers are whole numbers that can have more than 2 factors.

Answer: A sequence is a type of function. Remember, a function is any formula that can be expressed in "f(x) = x" format, but a sequence only contains integers at or greater than zero.

Hope this helps! Have a good day! :)

Answer:

One triangle

Step-by-step explanation:

I hope this helps :)

Answer:

Angle BFC is complimentary to AFB. Its measure is 12.

Step-by-step explanation:

Complementary angles add up to 90 degrees. When these two angles combine, it adds up to 90. 90-78 = 12. This angle's measure is 12.

Answer:

We know that to reverse a number, we should swap the numbers in TENS and ONES position. Therefore, the general form of its reverse 'ba' is (10 \times b) + a. Let us try to find the sum of both these numbers. Therefore, the sum of two-digit numbers and their reverse is always a multiple of 11.

Step-by-step explanation:

#carryonlearning

Brainlest me please

Answer:

post your question and someone will respond

Answer:

it would range between 11.28379... to 13.819765...

Step-by-step explanation:

the circle's area formula is pi * radius^2

so you make to equation, plugging the 100 and 150 into the circle's area

you get square root of (100/pi) which gets 11.28379... for the area of 100

you do the same with 150 to get square root of (150/pi) which gets 13.819765...

those are the diameter of the circle since the diameter is double the radius which i already multiplied afterwards. so if you need the radius divide the number ive given you

Answer:

The answer is true

Step-by-step explanation:

hope this helps

Answer:

  A, D

Step-by-step explanation:

You want to know the bound for the values of Sn and Tn, given their definitions as ...

  [tex]\displaystyle S_n=\sum_{k=1}^n{\dfrac{n}{n^2+kn+k^2}}\\\\T_n=\sum_{k=1}^{n-1}{\dfrac{n}{n^2+kn+k^2}}[/tex]

All we need to do to determine the correct answer choices is evaluate the sums for some value of n.

For n=2, the value of S2 is ...

  S2 = 2/(4+2+1) +2/(4+4+4) = 2/7 +2/12 = 19/42 ≈ 0.4524

For n=2, the value of T2 is ...

  T2 = 2/(4+2+1) = 2/7 ≈ 0.2857 . . . . . 1/(3n) less than the value of Sn

Both of these values are less than π/(3√3) ≈ 0.6046.

The correct answer choices are ...

  A) Sn < π/(3√3)

  D) Tn < π/(3√3)

__

Additional comment

For the purpose here, it is not necessary to determine the limiting value of either Sn or Tn. It is only necessary to demonstrate which side of the given value the terms of either sequence lie.

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Answer:

The power is 32 because that is what 2 to th 5 is , 2 is the base as its the number being multiplied 5 times which leaves 2 as the exponent.

Answer:

Step-by-step explanation:

Circumference is given by the formulas :

[tex]2\pi r[/tex] or [tex]\pi d[/tex]

Since we are given the diameter we can use the second one :

We are told to use 3.14 for π :

C = (3.14)×(16)

C = 50.24

Area of a circle is given by the formula:

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

To work out r we simply half the diamter:

16÷2 = 8

Now we put this into the area formula:

π(8)² = 64π

We are told to use 3.14 as pi so:

64π = 64×3.14 = 200.96

Answer:

Circumference = 50.24 in

Area = 200.96 in²

Step-by-step explanation:

First, let us find the circumference of the circle.

For that, let us use this formula.

C = π d

Given that,

d ⇒ diameter ⇒ 16 in

Let us find now.

C = π d

C = 3.14 × 16

C =  50.24 in

And now let us find the area of the circle.

Before that, let us find the radius.

d = 2r

16 = 2r

Divide both sides by 2.

8 in ⇒ radius

Let us use the below formula to find the area of the circle.

A = π r²

A = 3.14 × 8 × 8

A = 200.96 in²

Step-by-step explanation:

Here,let x = 1,2,3 and 4

Then,

Domain =(1,2,3,4)

Again,

f(1)= 3*1 + 5

=3 + 5

=8

f(2)=3*2 + 5

=6 + 5

=11

f(3)=3*3 + 5

=9 + 5

=14

f(4)=3*4 + 5

=12 + 5

=17

Therefore, Range=(8,11,14,17)

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5.7\\ h=10 \end{cases}\implies \begin{array}{llll} V=\pi (5.7)^2(10)\implies V=324.9\pi \\\\\\ V\approx 1020.7 \end{array}[/tex]

Look at the diagram for the answer

Hope that helps!

Step-by-step explanation:

[tex] \tan(31) = \frac{x}{33} \\ x = 33 \tan(31) \\ x = 19.82840042791 \\ x = 19.83[/tex]

Answer:

x = 19.8

Step-by-step explanation:

You want to use tangent, since you are trying to find the opposite side and know the adjacent side to the angle.

tan = opposite/adjacent

31tan = x/33

Multiply both sides by 33

33(31tan) = (33) x/33

33(31tan) = x

Find the tan of 31° using a scientific calculator.

tan 31° is about 0.6

Solve for x

33(0.6) = x

x = 19.83

rounded to the the nearest tenth

x = 19.8

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

Take (3x + 5) common in there :

[tex]\qquad \tt \dashrightarrow \:x(3x + 5) - 4(3x + 5)[/tex]

[tex]\qquad \tt \dashrightarrow (3x + 5) (x - 4)[/tex]

So, choice D is correct

Step-by-step explanation:

p(x)=x³-1

p(-1)=(-1)³-1=(-1)-1=(-2)

p(-1)=(-2)

p(1)=(1)³-1=1-1=0

p(1)=0