Which of these is the quadratic parent function

[tex]\bf \textit{sum of all \underline{interior angles} in a polygon}\\\\ S=180(n-2)~~ \begin{cases} n=\textit{number of sides}\\ \cline{1-1} n=24 \end{cases}\implies \begin{array}{llll} S=180(24-2)\\\\ S=3960 \end{array}[/tex]

Answer:

$2700.00

Step-by-step explanation:

6000 x 3% =180.00

180.00 x 15= 2700.00

To determine the probability that Harold buys an ice-cream on Wednesday, we consider the probabilities for each day. Given that he bought an ice-cream on Monday, there is a 40% chance that he will buy an ice-cream on Wednesday.

To determine the probability that Harold buys an ice-cream on Wednesday, we need to consider the probabilities for each day.

Given that he bought an ice-cream on Monday, there is a 30% chance that he will buy a drink on Tuesday and a 40% chance that he will buy an ice-cream on Tuesday.

Using the probabilities, we can calculate the probability that Harold buys an ice-cream on each day:

Monday: 1 (since he bought an ice-cream)

Tuesday: 0.4 (40% chance of buying an ice-cream based on previous ice-cream purchase)

Wednesday: 0.4 (40% chance of buying an ice-cream based on previous ice-cream purchase)

Answer : The true statements are:

The equation [tex]c+d=58[/tex] represents the sum of two numbers.

The equation [tex]c=\frac{d}{2}-8[/tex] represents the relationship between the two numbers.

The number c is, 14

The number d is, 44

Step-by-step explanation :

Given:

Let 'c' represent the first number. Let 'd' represent the second number.

The sum of two numbers is 58. The equation will be:

[tex]c+d=58[/tex]      .........(1)

The first number is 8 less than half the second number. The equation will be:

[tex]c=\frac{d}{2}-8[/tex]      .........(2)

Now by solving the two equations, we get the value of c and d.

As, [tex]c+d=58[/tex]

or, [tex]c=58-d[/tex]          ..........(3)

Now put equation 3 in 2, we get the value of d.

[tex]58-d=\frac{d}{2}-8[/tex]

[tex]58-d=\frac{d-16}{2}[/tex]

[tex]2(58-d)=d-16[/tex]

[tex]116-2d=d-16[/tex]

[tex]3d=132[/tex]

[tex]d=44[/tex]

Now put the value of 'd' in equation 3, we get the value of 'c'.

[tex]c=58-d[/tex]

[tex]c=58-44[/tex]

[tex]c=14[/tex]

Thus, the value of c and d is, 14 and 44 respectively.

Answer:

ABGH

Step-by-step explanation:

Answer:

B) 0,-2  (x = 0 , y = -2)

Step-by-step explanation by elimination:

Solve the following system:

{2 x + 6 y = -12 | (equation 1)

{5 x - 5 y = 10 | (equation 2)

Swap equation 1 with equation 2:

{5 x - 5 y = 10 | (equation 1)

{2 x + 6 y = -12 | (equation 2)

Subtract 2/5 × (equation 1) from equation 2:

{5 x - 5 y = 10 | (equation 1)

{0 x+8 y = -16 | (equation 2)

Divide equation 1 by 5:

{x - y = 2 | (equation 1)

{0 x+8 y = -16 | (equation 2)

Divide equation 2 by 8:

{x - y = 2 | (equation 1)

{0 x+y = -2 | (equation 2)

Add equation 2 to equation 1:

{x+0 y = 0 | (equation 1)

{0 x+y = -2 | (equation 2)

Collect results:

Answer:  {x = 0 , y = -2

Answer:

B

Step-by-step explanation:

what I did was I drew a square and folded it if both sides matched i knew that that was a line of symmetry

Answer:

B) 2

Step-by-step explanation:

Given that a rectangle is not a square.

Hence we find that opposite sides are equal.

If we mark midpoints on all sides then the vertical line joining mid points and horizontal lines joining next pair of midpoint of opposite sides are the lines of symmetry

There can be no other line of symmetry

Hence no of lines of symmetry for a rectangle = 2

Answer:

[tex]f(x)=-x^{2} +8x-16[/tex]

Step-by-step explanation:

we know that

A polynomial function that has a leading coefficient of -1 and root 4 with multiplicity 2 is equal to

[tex]f(x)=-(x-4)^{2}[/tex]

Expand the function

[tex]f(x)=-(x^{2}-8x+16)\\ \\f(x)=-x^{2} +8x-16[/tex]

Answer: B

Step-by-step explanation:

Let

x--------> volume of 50​% fertilizer

y--------> volume of 30% fertilizer

we know that

x+y=160-----> x=160-y-----> equation 1

x*0.5+y*0.3=160*0.4-----> equation 2

substitute equation 1 in equation 2

[160-y]*0.5+0.3*y=63.8----> 77-0.35*y+0.25*y=63.8

0.10*y=13.2------> y=13.2/0.10----> y=132 gal

x=220-y----> x=220-132----> x=88 gal

the answer is

88 gal of 50​% fertilizer

132 gal 30​% fertilizer

To obtain a 40% fertilizer mixture, the landscaping company should mix 80 gallons of 50% fertilizer with 80 gallons of 30% fertilizer.

To solve this problem, we can set up an equation based on the amount of fertilizer needed and the percentage of fertilizer in each type. Let's call the amount of 50% fertilizer x and the amount of 30% fertilizer y. We know that the total amount of fertilizer needed is 160 gallons, so we can write the equation x + y = 160. We also know that the amount of fertilizer in the 50% type is 0.5x and the amount of fertilizer in the 30% type is 0.3y. Since we want a total of 40% fertilizer, we can write the equation 0.5x + 0.3y = 0.4 * 160. Solving this system of equations will give us the amounts of each type of fertilizer needed.

First, let's rearrange the first equation to solve for x: x = 160 - y. Substituting this into the second equation, we get 0.5(160 - y) + 0.3y = 0.4 * 160. Simplifying the equation, we get 80 - 0.5y + 0.3y = 64. Combining like terms, we have 80 - 0.2y = 64. Subtracting 80 from both sides, we get -0.2y = -16. Dividing both sides by -0.2, we get y = 80. Now we can substitute this value back into the first equation to solve for x: x = 160 - 80 = 80. Therefore, they should mix 80 gallons of the 50% fertilizer with 80 gallons of the 30% fertilizer to obtain the desired 40% mixture.

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[tex]\displaystyle\\\int \limits_2^a(3x^2+x-1)\, dx=52\\\left|x^3+\dfrac{x^2}{2}-x\right|_2^a=52\\a^3+\dfrac{a^2}{2}-a-(2^3+\dfrac{2^2}{2}-2)=52\\a^3+\dfrac{a^2}{2}-a-(8+2-2)=52\\a^3+\dfrac{a^2}{2}-a-8=52\\a^3+\dfrac{a^2}{2}-a=60\\2a^3+a^2-2a=120\\2a^3+a^2-2a-120=0[/tex]

Now you need to solve the resulting equation, but it's not easy. The approx. solution is [tex]a\approx 3.8[/tex]

The exact solution is

[tex]a=\dfrac{1}{6}\left(-1+\sqrt[3]{6461-78\sqrt{6861}}+\sqrt[3]{6461+78\sqrt{6861}}\right)[/tex]

Answer:

a = 3.84

Step-by-step explanation:

Let's integrate the function

3x^2 becomes 3x^3/3 =x^3

x becomes x^2/2

-1 becomes -x

The intergral is x^3 +x^2/2 -x

We take the upper limit minus the lower limit

a^3 +a^2/2 -a - (2^3 + 2^2/2 -2) and that is equal to 52

Simplify

a^3 + a^2/2 -a - (8+2-2) = 52

a^3 +a^2/2 -a -(8) = 52

Subtract 52 from each side

a^3 +a^2/2 -a -8-52 = 52-52

a^3 +a^2/2 -a -60 =0

Multiply by 2

2a^3 +a^2 -2a -120 = 0

Using a graphing system, we see it only has 1 real root

This is at approximately

3.84

Check the picture below.

The formula that would be used to find the measure of angle 1 will be

m<1 =12(a - b)

To get the measure of angle 1, the circle theorem below will be used as shown:

The angle at the vertex of the circle is equal to half of the difference of the intercepted arc.

The formula that would be used to find the measure of angle 1 will be

m<1 =12(a - b)

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Answer:

[tex]\large\boxed{A.\ -9a^3b^2}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{-729a^9b^6}\qquad\text{use}\ \sqrt[n]{xy}=\sqrt[n]{x}\cdot\sqrt[n]{y}\\\\=\sqrt[3]{-729}\cdot\sqrt[3]{a^9}\cdot\sqrt[3]{b^6}\\\\=-9\cdot\sqrt[3]{a^{(3)(3)}}\cdot\sqrt[3]{b^{(2)(3)}}\qquad\text{use}\ (x^n)^m=x^{nm}\\\\=-9\cdot\sqrt[3]{(a^3)^3}\cdot\sqrt[3]{(b^2)^3}\qquad\text{use}\ \sqrt[3]{x^3}=x\\\\=-9a^3b^2[/tex]

Answer: A

Step-by-step explanation:

-9•9•9= -729a 9/3= 3

6/3=b^ 2

Answer:

71°

Step-by-step explanation:

The equation should be 19+90+x=180

Step 1: Add 19+90=109

Step 2: Subtract 180-109=71

So, you're answer is 71°

Final answer:

To find the measure of the other angle in a right triangle when one angle is given, subtract the given angle and the right angle from 180 degrees to get the third angle, which is the measure of the other angle.

Explanation:

One angle of a right triangle measures 19∘. In a right triangle, one angle is always 90 degrees. Therefore, to find the measure of the third angle, you need to subtract the sum of the given angle and the right angle from 180 degrees.

Third angle = 180° - 90° - 19° = 71°. So, the measure of the other angle in the right triangle is 71 degrees.

With $5 and pencils priced at 25 cents each, the student can buy 20 pencils. This is obtained by dividing $5 by $0.25 (the cost of one pencil).

Let's break down the calculation step-by-step:

Identify the given information.

The student has $5 to spend.

Each pencil costs 25 cents, which is equivalent to $0.25.

Set up the formula for the number of pencils.

Number of pencils = Total money / Cost per pencil

Substitute the given values into the formula.

Number of pencils = $5 / $0.25

Simplify the expression.

Dividing $5 by $0.25 is the same as multiplying $5 by the reciprocal of $0.25, which is 4.

Number of pencils = 5 * 4

Calculate the result.

Number of pencils = 20

So, the student can buy 20 pencils with $5.

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Answer:

The degree is 2.

Step-by-step explanation:

We are given f(x)=-3x^2 and g(x)=-4x+1.

(f o g)(x)

f(g(x))

f(-4x+1)

This means the old x in f will be replaced with -4x+1 like so:

-3(-4x+1)^2

-3(-4x+1)(-4x+1)

Use foil!

-3(16x^2-4x-4x+1)

-3(16x^2-8x+1)

-48x^2+24x-3

The degree is 2. The degree is the highest exponent on the variable if you only have one variable and your polynomial is written in standard form.

Answer:

[tex]8m^4n^5[/tex]

Step-by-step explanation:

cube root is basically taking to the power of  [tex]\frac{1}{3}[/tex]

Also, there is a property that is  [tex](x^m)^n=x^{mn}[/tex]

We can use these and find the cube root of the expression:

[tex](512m^{12}n^{15})^{\frac{1}{3}}\\=(512)^{\frac{1}{3}}*(m^{12})^{\frac{1}{3}}*(n^{15})^{\frac{1}{3}}\\=8*m^{\frac{12}{3}}*n^{\frac{15}{3}}\\=8*m^4 * n^5[/tex]

Thus, third answer chioce is right.

Answer:

C. 8m^4n^5[/tex]

Step-by-step explanation:

We are given [tex]\sqrt[3]{512m^{12}n^{15}  }[/tex]

The cube root is nothing but the power of [tex]\frac{1}{3}[/tex]

Now we have to write 512 as the power 3.

512 = 8.8.8 = [tex]8^{3}[/tex]

So, [tex]\sqrt[3]{512m^{12}n^{15}  }[/tex] = [tex](8^{3}.m^{12}.n^{15})   ^{\frac{1}{3}}[/tex]

We know that the exponent property: [tex](a^{m} )^n= a^{mn}[/tex]

Using this property, we can simplify the exponents.

= [tex]8.m^{4} .n^5 = 8m^4n^5[/tex]

Answer:

t x 6=c or      c divided by 6= t

Step-by-step explanation:

Answer: [tex]c=6t[/tex]

Step-by-step explanation:

You need to analize the information provided in the exercise:

-  "c" represents the number of chairs in the conference room.

- "t" represents the number of tables in the conference room.

- "6 times the number of tables" indicates a multiplication. This is:

[tex]6t[/tex]

Therefore if the number of chairs in the conference room is equal to 6 times the number of tables, you can write this equation that matches the information provided:

[tex]c=6t[/tex]

Final answer:

To graph the scenario where the number of loaves of bread on hand (L) minus the number of reservations (R) must be greater than 5, one would represent this inequality on a two-dimensional graph with L on the horizontal axis and R on the vertical axis, shading the region above the line L - R = 5.

Explanation:

The subject of the question is Mathematics, with a focus on inequalities and graphical representation of constraints. The scenario describes the requirement that the number of loaves of bread on hand minus the number of reservations must be greater than 5. To represent this mathematically, let's define the variable L as the number of loaves of bread on hand and R as the number of reservations. The inequality can, therefore, be expressed as L - R > 5.

This inequality needs to be represented on a graph. To do this, one typically uses a two-dimensional coordinate system where the horizontal axis, often labeled as x, could represent the number of loaves of bread (L), and the vertical axis, often labeled as y, could represent the number of reservations (R). The region that satisfies the inequality L - R > 5, would be shaded above the line L - R = 5 (since we are looking for L being greater than R by more than 5 units). This line will have a slope of 1 and a y-intercept at R = -5.

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=113.04 \end{cases}\implies 113.04=\pi r^2\implies \cfrac{113.04}{\pi }=r^2 \\\\\\ \stackrel{using~\pi =3.14}{36}=r^2\implies \sqrt{36}=r\implies 6=r[/tex]

Answer:

The arcs form a circle ⇒ answer C

Step-by-step explanation:

* Lets explain some facts in the circle

- The chord in a circle is a segment whose endpoints lie on the circle

- Any chord of a circle intersects it into 2 arcs

- The minor arc which its measure lies between 0° and 180°

-The major arc which its measure lies between 180° and 360°

- The sum of the measures of the minor arc and the major arc is equal

  to the measure of the circle

- The measure of the circle is 360°

* Lets solve the problem

∵ The measure of arc XY + the measure of arc YZX = 360°

∵ The arcs do not overlap

- That means the endpoints of the arcs are X and y

∵ The measure of the circle is 180°

∴ The arcs form a circle

Answer:circle

Step-by-step explanation:

im lookin it on a question rn

Answer:

F 24

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

10^2 + EF^2 = 26^2

100 + EF^2 = 676

Subtract 100 from each side

100-100 + EF^2 = 676-100

EF^2 = 576

Take the square root of each side

sqrt(EF^2) = sqrt(576)

EF = 24

Answer:

F 24

Step-by-step explanation:

You have to use the Pythagorean Theorem

a²+b²=c²

(a and b are the legs of the triangle and c is always the hypotenuse)

a²+10²=26²

a²+100=676; now isolate the a² by subtracting 100 from both sides.

a²=576; now square root each side (gets rid of the squared)

a=24

Answer:

Z=1.055

Step-by-step explanation:

Z is inversely proportional to X: [tex]Z=\frac{K}{X}[/tex] Where K is a constant

X=18, Z=1.583333333333 we can find K value

K=Z*X =1.58333333333*12= 19

So, Using X=18 We have the following

[tex]Z=\frac{19}{18}[/tex]= 1.055

Answer:

$300

Step-by-step explanation:

Let's say that L is the amount of money Luisa had in the beginning, and C is the amount of money Connor had in the beginning.

C + L = 360

C - 2/5 C = L + 2/5 C

Simplifying the second equation:

3/5 C = L + 2/5 C

1/5 C = L

Substituting into the first equation:

C + 1/5 C = 360

6/5 C = 360

C = 300

Connor originally had $300, and Luisa $60.  Connor gave Luisa $120, and they both had $180.

The graph that represents y = -|x + 4| + 1 is graph (a)

The equation is given as:

y = -|x + 4| + 1

The above equation is a transformation from the parent function, which is represented as:

y = |x|

First the function is reflected across the x-axis, then translated 4 units left, and lastly 1 unit up.

The graph that represents this transformation is graph (a)

Hence, the graph that represents y = -|x + 4| + 1 is graph (a)

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Answer:

12

Step-by-step explanation:

For our problem since we only in 10 am:

I'm going to let x=4 represent the time 10:04 am

which means I'm going to let x=17 represent 10:17am.

So when x=4, y=23 miles and when x=17,y=179 miles.

You have two points.

You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Or just line the points up vertically and subtract them vertically, then put 2nd difference over first difference. Like this:

(    17  ,   179)

-(     4 ,      23)

-----------------------

   13          156

So the slope is 156/13=12 miles/hour.

Answer:

Step-by-step explanation:

Sometimes, it is easiest to let a calculator do the work. (See below)

__

The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.

You can also use the identities ...

  cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)

  cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)

  cos(2θ) = 7/25

__

  tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)

  tan(2θ) = -24/7

Answer: tan(2θ) = -24/7

Step-by-step explanation: N/A

Answer: B

Step-by-step explanation:

This is because it is just a statement, and may be true for some people, but not others.

Answer:

True.

Step-by-step explanation:

These are sets containing the same exact elements so they are the same set of elements.

They both contain 4 elements.

The 4 elements in each are c, f , j , and k.

It matters not of the arrangement.  It also doesn't matter if they repeat an element.  

For example these sets are also the same:

{a,a,b} and {a,b}.

They both contain 2 elements and those elements are a and b.

People don't normally write something like {a,a,b} because it is redundant (because of the repetition of a).  

Here is an example of some sets that are equal:

{1,2,3}={1,3,2}={2,1,3}={2,3,1}={3,1,2}={3,2,1}.

These are all the same because they all contain the elements: 1 , 2 , and 3. It doesn't matter the order in a set.

Answer:

Option C is correct.

Step-by-step explanation:

The given function f(x) is:

f(x) = x^2 + 22x + 58

To find the vertex find [tex](\frac{-b}{2a} )^2[/tex] and add and subtract it from both sides of the given function

b= 22, a= 1

Putting values:

[tex](\frac{-b}{2a} )^2 = (\frac{-22}{2(1)})^2\\=(\frac{-22}{2})^2\\= (-11)^2\\=11^2[/tex]

Adding (11)^2 on both sides

f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2

f(x) = x^2+22x+(11)^2 +58-(11)^2

a^2 +2ab+b^2 = (a+b)^2 Using this formula:

f(x)=(x+11)^2+58-121

f(x)=(x+11)^2-63

The vertex of the given function is (-11,-63)

The function is translated 4 units to right and 16 units up

The vertex of new function will be:

(x+4,y+16) => (-11+4,-63+16)

=> (-7,-47)

So, the vertex of new function is  (-7,-47)

The function will be

(x+7)^2 -47

So, Option C is correct.

Answer:

C

Step-by-step explanation: