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E and F

The standard form for a quadratic function is f(x) = ax^2 + bx + c.

E follows this pattern. a = -2; b = -8; c = 3

F also follows this pattern. a = 1/2; b = -2; c = 0

Answer:

A. (first choice)

Step-by-step explanation:

Examine all options:

A. The diagram shows the arc (1/4 from a circle). While rotating this arc about the given axis, we get the hemisphere.

B. The diagram shows the semicircle (1/2 from a circle). While rotating this semicircle about the given axis, we get the whole sphere.

C. The diagram shows the segment (perpendicular to the axis). While rotating this segment about the given axis, we get the circle (lying in a plane).

D. The diagram shows the segment. While rotating this segment about the given axis, we get the cone.

Answer:

W = 415

Step-by-step explanation:

Is means equals and of means multiply

W = 125% * 332

Change to decimal form

W = 1.25 *332

W = 415

Answer:

  44.1 cm

Step-by-step explanation:

In order to find the length of side "a", you need to know the measure of angle A. That is found by making use of the fact that the sum of angles in a triangle is 180°.

  102° + 28° + A = 180°

  A = 180° -130° = 50°

Now, you can fill in the given information in the given equation and solve for "a":

  sin(A)/a = sin(B)/b

  sin(50°)/a = sin(28°)/(27 cm)

Multiplying by a(27 cm) gives ...

  sin(50°)(27 cm) = a·sin(28°)

Dividing by the coefficient of "a", we get ...

  a = (27 cm)sin(50°)/sin(28°) ≈ 44.0563 cm

Rounded to the nearest tenth, this is ...

  a ≈ 44.1 cm

_____

Since we're looking for a side length (not an angle), I prefer to write the Law of Sines formula "upside down" from that shown:

  a/sin(A) = b/sin(B) = c/sin(C)

Then it is one step to get to ...

  a = b·sin(A)/sin(B) . . . . . . multiply by sin(A)

Answer:

(a) y = ±(√x)/2

Step-by-step explanation:

You want to find y such that ...

x = f(y)

x = 4y^2 . . . . . . . put in the expression for f(y)

x/4 = y^2 . . . . . . .divide by 4

±√(x/4) = y . . . . . take the square root

y = ±(√y)/2 . . . . . simplify

Perimeter is the distance around an object, so you would add 5+9+11 to get 25 cm

Answer:

  462 cm^2

Step-by-step explanation:

The centerline of the cloth area has a radius of (28 cm + 14 cm)/2 = 21 cm, so its length will be 1/4 of the circumference of a circle of that radius:

  cloth centerline length = (1/4)·2πr = (π/2)·21 cm = (22/7)/2 · 21 cm = 33 cm

The width of the cloth portion is ...

  28 cm - 14 cm = 14 cm

so the area of the cloth portion will be the product of centerline length and width:

  (33 cm)(14 cm) = 462 cm^2

Answer:

  n = -2

Step-by-step explanation:

Eliminating parentheses, you have ...

  2n +6 -6n = 14

Combining terms and subtracting 6, you get ...

  -4n = 8

Dividing by the coefficient of n gives ...

  n = -2

_____

Check

  2(-2) +3(2 -2(-2)) = 14

  -4 +3(2+4) = 14

  -4 +3(6) = 14

  -4 +18 = 14 . . . . answer checks OK

Answer:

  178,334 pens

Step-by-step explanation:

The company makes $0.30 above the variable cost on each pen, so must sell $53,500/$0.30 ≈ 178,334 pens to cover the cost of operation.

_____

Sale of 178,333 pens will result in a total cost of $0.10, so doesn't quite make the company break even. Sale of 178,334 pens will result in profit of $0.20.

Answer:

  B.  C(x) = 0.02(x - 360)2 + 300

Step-by-step explanation:

The minimum of a quadratic function is found at its vertex. The vertex form of the equation lets you read the coordinates of the vertex directly, so that is the form most helpful for finding minimum cost.

___

Perhaps the next most helpful form is that of option D, sometimes called "intercept form." The vertex is located halfway between the intercepts, so will be halfway between 0 and 720. Of course, the vertex location at 360 is read directly from the vertex form of option B.

Answer:

A

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  x^2 (not x2).

To determine the number of t-shirts that would minimize cost, we'd want to have a quadratic function graph that opens up, and to determine the vertex (which point would also be the minimum cost).

Equation A is the one we want.  Why?  because we can ignore the coefficient 0.02 in determining the minimum cost.  We see immediately that the coefficient of the x^2 term is a = 1 and that of the x term is b = -720.

Recall that the axis of symmetry passes through the vertex / minimum, and has equation

                                                                        720

x = -b / (2a).  With a = 1 and b = -720,   x = - --------- = 360

                                                                           2

Again, A is the correct answer.  The miminim cost occurs at x = 360 (shirts).

Answer:

a(h) = 1.25h²

Step-by-step explanation:

The formula for the area of a rectangle is ...

A = HW . . . . . where H represents the height and W represents the width

If the image has a height of h, then the width is 1.25 times that, or 1.25h. Putting these values into the formula, we have ...

A = h·(1.25h)

A = 1.25h²

In function form, we can write a(h), area as a function of height, as ...

a(h) = 1.25h²

Answer:

  The 6% simple interest account earns more interest in 2 years.

Step-by-step explanation:

You can compare the multipliers in the interest formulas.

For simple interest, the amount in the account (A) starting with principal P and earning at rate r for t years will be ...

  A = P(1 +rt)

For the values given, r=.06 and t=2, the multiplier is ...

  1 +rt = 1 +.06·2 = 1.12

__

For interest compounded annually, the amount will be ...

  A = P(1 +r)^t

For the given values, the multiplier is ...

  (1+r)^t = (1.04)^2 = 1.0816

__

Since 1.12 > 1.0816, the account earning simple interest will earn more interest.

The range of the function g(x)=6/x is the same as the range of the parent function f(x)=1/x, which is all real numbers except zero, despite the scaling factor '6'. This is because transformations other than shifts do not change the range.

The comparison between the functions g(x)=6/x and f(x)=1/x lies in the understanding of how modifications to a parent function affect its range. The function f(x)=1/x is a parent function and its range is all real numbers except for zero. This is because as x approaches zero, the output of the function approaches infinity, thus, zero is not included in the range.

When we look at the function g(x)=6/x, the multiplier '6' just scales the values of the parent function by a factor of 6. This means the range will still be all real numbers except for zero, just like in the parent function. This is because the function transformations do not affect the range of the function that has a rational form like f(x)=1/x unless there are additional horizontal or vertical shifts.

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Answer:

B

Hope This Helps!   Have A Nice Day!!

Answer:

b

Step-by-step explanation:

Answer:

The measure of angle JKP is 61°

Step-by-step explanation:

we know that

If the measure of angle m<LOI=38°

then

m arc IL=38° -----> by central angle

and

If the measure of angle m<JOP=84°

then

m arc JP=84° -----> by central angle

Remember that

The measure of the interior angle is the semi-sum of the arcs that comprise it and its opposite.

so

m<JKP=(1/2)[arc IL+arc JP]

substitute the values

m<JKP=(1/2)[38°+84°]=61°

Answer:

  745.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the trig function relating the hypotenuse and the side opposite an angle. It tells you ...

  Sin = Opposite/Hypotenuse

The line marked x (the hypotenuse of the triangle) is a transversal crossing the two parallel horizontal lines. That means the interior angle of the triangle at lower right (the angle of elevation) has the measure 28°. That angle is opposite the side marked 350 ft. So, you have ...

  sin(28°) = (350 ft)/x

Multiplying by x/sin(28°), this equation becomes ...

  x = 350 ft/sin(28°)

  x ≈ 745.5 ft

Let's call the two numbers x and y.

We know that x+y = 842 and that x-y = 314

Now that we have two equations, we can solve using substitution by solving for one variable in one of the equations, and plugging that in for the same variable in the other equation.

Lets solve for x in the second equation to get:

x = 314 + y

Now plug in 314+y for x in the first equation:

(314 + y) + y = 842

Combine like terms:

314 + 2y = 842

Now solve for y:

2y = 842-314

2y = 528

y = 264

Finally, plug 264 in for y to solve for x:

x + 264 = 842

x = 842-264

x = 578

The two numbers are 578 and 264.

please attached is your answer

Answer:

  42.5 ft by 21.3 ft

Step-by-step explanation:

The largest area is obtained when half the available fence is used parallel to the existing fence, and the other half is used to fence the two ends of the rectangle. Here, that means the dimension parallel to the existing fence is ...

  (85 ft)/2 = 42.5 ft

and the ends of the rectangular garden are ...

  (42.5 ft)/2 = 21.25 ft ≈ 21.3 ft

_____

You can figure this as follows:

Let x represent the length of fence parallel to the existing fence. Then the other dimension of the fenced area is (85 -x)/2 and the fenced area is the product of these dimensions.

  area = x(85-x)/2

This expression describes a downward-opening parabola with zeros at x=0 and at x=85. The vertex (maximum) will be found where x is halfway between these values, at x = (0 +85)/2 = 42.5.

Area is maximized when 42.5 ft of fencing is used parallel to the existing fence, and the other half of the fencing is used for the other two sides of the enclosure.

Answer:

44.444%, (B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)

Step-by-step explanation:

We will start with the second part of the question, listing out all of the possible combinations that can occur from this data set.  There is a 50/50 chance of having a girl or a boy, and there are three children.  For now we'll use B to represent a boy and G for a girl.  It goes as follows:

(B, B, B), (B, B, G), (B, G, B), (B, G, B), (B, G, G), (G, B, B), (G, B, G), (G, G, B), (G, G, G)

I often find it easy to write out a branch diagram to help me visualize this problem and make sure I have all possibilities. (See attached image)

Count the total number of combinations (9).  Next, count the number that include exactly 2 girls (4).  With this information, we now know that there is a 4 out of 9 chance of having exactly 2 girls and one boy.  4/9 is in simplest form, so all you have to do is find the percentage (44.444%)

Answer:

C or .375

Step-by-step explanation:

Answer:

15°

Step-by-step explanation:

If CB is a diameter, the arc BKAC is a semicircle and has a degree measure of 180.  If the measure of angle BCK is 20 and it is an inscribed angle, then the measure of the arc it intercepts is twice that.  So arc BK measures 40 degrees.  That means that arc KA has a measure that is found by subtracting arc AC and arc BK from 180.  180 - 40 - 110 = 30.  If that arc is 30 and the angle that intercepts it is inscribed, then the angle measure is half the measure of the arc. So the angle is 15°

ANSWER

Option A

EXPLANATION

The graph of g(x) has equation:

[tex]g(x) = \sqrt[3]{ x + 2 } - 4[/tex]

The parent function is

[tex]f(x) = \sqrt[3]{x} [/tex]

To obtain the graph of g(x), we must shift f(x) 2 units to the left and 4 units down.

The graph of this function is shown in the attachment.

The correct choice is option A.

Answer:

x = ab/c

Step-by-step explanation:

The product of the distances from the point of intersection of the chords (secants) to the circle is the same for both chords (secants). (This is true whether the point of intersection is inside or outside the circle.)

ab = cx

x = ab/c

Answer:-

Central angle , Ф/2π , A = Ф/2 r²

The ratio is 1/3 , V = 1/3 Bh

The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

Step-by-step explanation:

* Lets revise the rules of the area of the sector of a circle

- The area of the sector which has a central angle Ф° is

  (Ф°/360°) × πr², where 360° is the measure of the circle and r is

  the radius of the circle

- The area of the sector which has a central angle Ф radians is

  (1/2) r²Ф

* Lets complete the missing in the 1st picture

- The ratio of the sector's area A to the circle's area is equal to the

  ratio of the central angle to the measure of a full rotation of the circle

- A full rotation of a circle is 2π. This proportion can written as

 A/πr² = Ф/2π

- Multiply both sides by πr² to get A = Ф/2 r² where Ф is the measure

 of the central angle and r is the radius of the circle

* Lets revise the rules of the volume of the prism and the volume

 of the pyramid, where they have the same base and height

- The volume of the prism = area of the base × its height

- The volume of the pyramid = 1/3 × area of the base × its height

- From them the ratio of the volume of the pyramid to the volume

 of the prism is 1/3

- The formula of the volume of the prism is V = Bh, where B is the

  area of the base and h is the height, the formula of the volume

  of the pyramid is V = 1/3 Bh

* Lets revise the standard form of the equation of a circle with

 center (h , k) and radius r

- The equation is: (x - h)² + (y - k)² = r²

∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0

∵ x² - 8x + y² - 2y - 8 = 0

- Lets equate the two equation

∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0

∵ -2h = -8 ⇒ ÷ -2

∴ h = 4

∵ -2k = -2 ⇒ ÷ -2

∴ k = 1

∵ h² + k² - r² = -8

∴ (4)² + (1)² - r² = -8

∴ 16 + 1 - r² = -8

∴ 17 - r² = -8 ⇒ subtract 17 from both sides

∴ -r² = -15 × -1

∴ r² = 25

* Substitute the values of h , k , r in the equation of the standard

 form of the circle

∴ (x - 4)² + (k - 1)² = 25

* The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

let's say is "x", so "x" is then 100% of the whole bill.

we know 15% is 22.05, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 22.05&15\\ x&100 \end{array}\implies \cfrac{22.05}{x}=\cfrac{15}{100}\implies 2205=15x \\\\\\ \cfrac{2205}{15}=x\implies 147=x[/tex]

Answer:

$147

Step-by-step explanation:

15% over 100 is .15

So you get .15x= 22.05

Get x by itself by dividing .15 by .15

whatever you do to one side you have to do to the other so divide 22.05 by .15 and you get $147

Answer:

400,000,000

Step-by-step explanation:

4000000000000×.0001 is the answer above

Answer:

[tex]4 \times {10}^{8 }m \: or \: 400,000,000m[/tex]

Step-by-step explanation:

Put them both into standard form.

[tex]0.0001 = 1 \times {10}^{ - 4} \: and \: 4 \: trillion \: is \: 4 \times {10}^{12} [/tex]

Multiply them together.

[tex](1 \times {10}^{ - 4} ) \times (4 \times {10}^{12}) = 4 \times 10^{8} [/tex]

Answer:

4 to 13

4:13

Step-by-step explanation:

I finished my test and these were the answers

The ratio of the number of fish to the total number of pets Dalia has is 4 to 13 or 4:13.

The subject of this question is the calculation of a ratio. In this case, the asked ratio is the number of fish to the total number of pets that Dalia has. Dalia has 4 fish and a total of 9 hamsters + 4 fish = 13 pets. Therefore, the correct answer is the ratio of 4 (fish) to 13 (total pets). This ratio can be represented in two ways: B) 4 to 13 or E) 4:13. The other options represent different ratios and do not correctly answer the question.

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Answer:

[tex]y=\frac{1}{12}(x+5)^2+2[/tex]

Step-by-step explanation:

We start with the standard form of a parabola which is

[tex](x-h)^2=4p(y-k)[/tex]

We know h and k from the vertex, we just need to solve for p and then simplify the equation.  P, by definition, is the distance between the directrix and the vertex.  That is 3 units.  So p = 3.  Fitting that into our equation along with h and k gives us:

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

Divide both sides by 12, then add the 2 to both sides and we have our parabola!

Answer:

see below for explanation

3x +2y = 15

Step-by-step explanation:

The x-coordinate and the y-coordinate are both linear functions of t, so their relationship to each other is linear. A graph of those (x, y) points must be a line.

___

You can find an equation by solving one of the expressions for t, then substituting that into the other.

x = 2t +3

t = (x -3)/2

Substituting into the y expression, we get ...

y = 3 -3(x -3)/2

y = (-3/2)x + 15/2

3x +2y = 15 . . . . . . . add 3/2x and multiply by 2 to put into standard form

_____

The attached graph shows a portion of the line defined parametrically (0 ≤ t ≤ 1). It is dotted so you can see it overlays the line defined by the linear equation in x and y.

Answer:

113 inches^2

Step-by-step explanation: