Someone plz help me with this

Answer:

[tex]\boxed{\text{C. }{f(x) =3(x + 2)^{2} - 1}}[/tex]

Step-by-step explanation:

The vertex form of a quadratic function

ƒ(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

You convert ƒ(x) = 3x² + 12x + 11 to the vertex form by completing the square.

Step 1.  Move the constant term to the other side of the equation

y - 11 =3x² + 12x

Step 2. Factor out the leading coefficient

y - 11 =3(x² + 4x)

Step 3. Complete the square on the right-hand side

Take half the coefficient of x, square it, and add it to each side of the equation.

4/2 = 2; 2² = 4

y – 11 + 12 =3(x² + 4x  + 4)

Note that when you completed the square by adding 4 inside the parentheses, you were adding 3×4 to the right-hand side, so you had to add 12 to the left-hand side.

Step 4. Simplify and write the right-hand side as a perfect square

y + 1 = 3(x + 2)²

Step 5. Isolate the y term

Subtract 1 from each side

y = 3(x + 2)² -1

[tex]\text{The vertex form of the equation is }\boxed{\mathbf{f(x) =3(x + 2)^{2} - 1}}[/tex]

If you compare this equation with the general vertex form and with the graph, you will find that h = -2 and k = -1, so the vertex is at (-2, -1).  

The quadratic equation f(x) = 3x^2 + 12x + 11 can be rewritten in vertex form as C. f(x) = 3(x + 2)^2 - 1 after completing the square.

The function f(x) = 3x2 + 12x + 11 can be rewritten in vertex form, which is y = a(x - h)2 + k, where (h, k) represents the vertex of the parabola. To convert the given quadratic to vertex form, we need to complete the square:

So, the correct vertex form of the equation is C. f(x) = 3(x + 2)2 - 1.

Answer:

X=57/37 , X=1.540

Answer:

n > 2

Step-by-step explanation:

-10 − -3n > -4

-10 + 3n > -4

3n > 6

n > 2

Check our answer: if n = 3:

-10 − -3(3)

-10 − -9

-10 + 9

-1

-1 > -4

-10 - (-3n) > -4 ---> -10 + 3n > -4

^^^^ -3n became positive because a negative times a negative gives a positive

Step 1: Combine like terms

normal numbers go with normal numbers. This would be -10 and -4. To get -10 to the right side of the inequality you must add 10 to both sides

(-10 + 10) + 3n > (-4 + 10)

(0) + 3n > 6

3n > 6

Step 2: Isolate n by dividing 3 to both sides of the inequality

[tex]\frac{3n}{3} > \frac{6}{3}[/tex]

n > 2

Hope this helped!

If you mean -10.0 - (-2.3) then the answer is -7.7

Final answer:

To subtract -10.0 - (-2.3), you change the subtraction of the negative number to addition and calculate -10.0 + 2.3, resulting in -7.7.

Explanation:

Subtracting a negative number from another negative number is equivalent to adding the absolute value of the number being subtracted. To solve the given problem, we can visualize it as negative 10.0 plus 2.3.

The subtraction of two negative numbers can be transformed into an addition problem by remembering that subtracting a negative is the same as adding a positive. Here is how you would calculate it step-by-step:

Start with the first number: -10.0.

Change the subtraction to addition because subtracting a negative is like adding a positive.

Add the absolute value of the second number: +2.3.

Combine both numbers: -10.0 + 2.3 = -7.7.

So, negative 10.0 minus (negative 2.3) equals -7.7.

Answer:

No, The answer should be 240

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

Answer b:

Step-by-step explanation:

Check the picture below.

so then, the highest point will be at the y-coordinate of its vertex.

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+48}t\stackrel{\stackrel{c}{\downarrow }}{+4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\bf \left( \qquad ,~~4-\cfrac{48^2}{4(-16)} \right)\implies \left( \qquad ,~~4+\cfrac{2304}{64} \right)\implies (\qquad ,~4+36) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\qquad ,~~\stackrel{\stackrel{\textit{how high}}{\textit{it went}}}{40})~\hfill[/tex]

Answer:

True for all b

Interval notation; (-∞, ∞)

Step-by-step explanation:

We have been given the following inequality;

26+6b>2(3b+4)

The first step is to open the brackets on the right hand side;

26+6b>6b+8

26-8>6b-6b

18>0

Since 18 is actually greater than 0, the solution set to the inequality is;

True for all b.

2[-2 + 3x]\3 + 2x² is the simplification.

Answer:

D) 5985

Step-by-step explanation:

Total area: 150×100 = 15000

Area for stars: 6×6 = 36

Total area - area for stars = area for fans

15000-36= 14964

14964ft² for fans, each takes up 2.5 ft²

14964 ÷2.5 = 5985.6 fans

Since we can't have 0.6 of a person, we round down to 5985 fans

Answer:

5,985 fans

Step-by-step explanation:

First you will need to get the floor area of the store

The dimensions are:

150' by 100'

This is 150 ft by 100 ft

Area would be:

Side x side (Assuming that the floor area is a quadrilateral)

150 ft x 100 ft = 15000 ft²

Next we solve for the area of the stars only:

6' by 6'

Side x side

6 ft x 6 ft = 36 ft²

So here we subtract the stars only area from the total floor area:

15,000 ft² - 36 ft² = 14,964 ft²

This is the floor area that the fans can occupy.

Next since the fire marshal said 1 person must occupy an area no less than 2.5ft², we divide the floor area for fans by the requirement.

14,964 ft²  = 5,985.6 fans

   2.5ft²

Since we cannot have a decimal for people, we need to round it down. If it goes beyond 5,985.6 that means we do not meet the minimum requirement of 2.5 ft² per person. So we need to round it down, to the nearest whole number, the answer would be:

5,985 fans.

Answer:

26.04cm^2

Step-by-step explanation:

28 divided by 20 is 1.4. 1.4 times the area will give you the area of the other figure. 1.4 x 18.6 = 26.04

use scale faction to solve and you get

36.5cm^2!

Answer:

[tex]LW=17.5\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle LAY

Find the measure of side LY applying the Pythagoras Theorem

[tex]LY^{2} =3.5^{2}+ 7.0^{2} \\ \\ LY^{2} =61.25\\ \\ LY=\sqrt{61.25}\ units[/tex]

Find the cosine of angle ALY

[tex]cos(<ALY)=\frac{LA}{LY}[/tex]

[tex]cos(<ALY)=\frac{3.5}{\sqrt{61.25}}[/tex] -----> equation A

In the right triangle LWY

[tex]cos(<ALY)=\frac{LY}{LW}[/tex]

[tex]cos(<ALY)=\frac{\sqrt{61.25}}{LW}[/tex] -----> equation B

equate equation A and equation B and solve for LW

[tex]\frac{3.5}{\sqrt{61.25}}=\frac{\sqrt{61.25}}{LW}[/tex]

[tex]LW=(\sqrt{61.25})(\sqrt{61.25})/3.5[/tex]

[tex]LW=17.5\ units[/tex]

Answer:

There

Step-by-step explanation:

Answer:

(5,-6)

Step-by-step explanation:

When you write the equation of a circle in the form

[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]

Then the center of the circle will be [tex](x_0,y_0)[/tex] and the radius will be [tex]r[/tex].

Answer:  The center of the given circle is (5, -6).

Step-by-step explanation:  We are given to find the center of the circle represented by the following equation :

[tex](x-5)^2+(y+6)^2-4^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the STANDARD equation of a circle with center (h, k) and radius r units is given by

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

From equation (i), we have

[tex](x-5)^2+(y+6)^2=4^2\\\\\Rightarrow (x-5)^2+(y-(-6))^2=4^2.[/tex]

Comparing with the standard form, we get that the center of the given circle is (h, k) = (5, -6).

Thus, the center of the given circle is (5, -6).

Here the answer is in this picture

Answer:

1. Ratio is 1 : 3

Step-by-step explanation:

1. The average salary for a professional baseball player in the United States can be approximated by = [tex]283(1.2)^{t}[/tex]

Where t = 0 represents the year 1984.

Salary in year 1988 = [tex]283(1.2)^{4}[/tex]  [t = 4 years]

Salary in year 1994 = [tex]283(1.2)^{10}[/tex] [t = 10 years]

Ratio of the average salary in 1988 to the average salary in 1994 = [tex]\frac{283(1.2)^{4}}{283(1.2)^{10}}=\frac{(1.2)^{4}}{(1.2)^{10}}[/tex]

= [tex]\frac{1}{(1.2)^{10-4}}=\frac{1}{(1.2)^{6}}[/tex]

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

2. Corrected form

[tex]\frac{x^{-9} }{x^{-3}}[/tex]

= [tex]x^{-9+3}[/tex][since [tex]\frac{a^{1}}{a^{1}}=a^{1-1}=a^{0}=1[/tex]]

= [tex]x^{-6}[/tex]

= [tex]\frac{1}{x^{6}}[/tex]  [ since [tex]\frac{1}{a^{1}}=a^{-1}[/tex] ]

Now we can compare the corrections and errors in the highlighted form.

Expression needs correction

[tex]\frac{x^{-9} }{x^{-3}}[/tex]

= [tex]x^{-9-3}[/tex]

=  [tex]x^{-12}[/tex]

= [tex]\frac{1}{x^{-12}}[/tex]

[(-10+2)-1]+(2+3)​ is equal to -4.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

Given

[(-10+2)-1]+(2+3)

Using BODMAS

= [-8 - 1] + 5

= -9 + 5

=-4

Therefore, [(-10+2)-1]+(2+3)​ is equal to -4.

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Final answer:

The value of the expression [(-10+2)-1]+(2+3) is found by following the order of operations; handle the parentheses first, then sum the results, which leads to a final answer of -4.

Explanation:

Step-by-Step Solution to the Expression

To find the value of the expression [(-10+2)-1]+(2+3), you follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

First, solve inside the parentheses: (-10+2) gives you -8.

Next, (-8-1) simplifies to -9, so now you have [-9].

Then, you solve the addition within the other set of parentheses: (2+3) which equals 5.

Finally, you add the results of the two sets of parentheses: -9 + 5.

Following addition rules for numbers with opposite signs, you subtract the smaller number from the larger one and keep the sign of the larger number, which in this case is negative. Thus, -9 + 5 equals -4.

Therefore, the value of the expression is -4.

Answer:

I did this test. The answer to this question is c.multiply each side by 4

Step-by-step explanation:

we'd do the same as before on this one as well.

if we take 27.99 to be the 100%, what is 12 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 27.99&100\\ 12&x \end{array}\implies \cfrac{27.99}{12}=\cfrac{100}{x}\implies 27.99x=1200 \\\\\\ x=\cfrac{1200}{27.99}\implies x\approx 42.87[/tex]

The discount rate can be determined by dividing the discount by the retail price, then multiplying by 100 to get the percentage. In this instance, the discount rate calculates to be approximately 42.87%.

To find the discount rate, you must first understand that it is the difference between the retail price and the sale price, divided by the retail price, and then multiplied by 100 to turn it into a percentage.

In this case, let's use the numbers from the problem. The retail price is $27.99 and the discount is $12, leaving a sale price of $15.99. We already know the discount is $12, so to find the rate we divide $12 (the discount) by $27.99 (the original price), and then multiply by 100.

Doing the calculation, ($12/$27.99) * 100 = approx. 42.87%. So the discount rate is approximately 42.87%.

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Answer:

B. the 15,559 residents

Step-by-step explanation:

I just took the final exam

The football, kicked by a football player during a practice, is in the air for approximately 3.79 seconds based on the model h = -4(4t - 11)^2.

The question asks for the duration that the football is in the air. This problem involves solving a quadratic function to determine the time when the height of the ball is zero, i.e., when it hits the ground again. The mentioned equation and given information form a quadratic equation.

The equation h = -4(4t - 11)^2 models the height of the football at any given time. The football is on the ground when h = 0. If we substitute h = 0, the equation becomes -4(4t - 11)² = 0. Using the quadratic formula, we find two solutions t = 0.54 s and t = 3.79 s.

As we are looking for the total time that the football is in the air, we are interested in when it falls back to the ground which corresponds to the larger solution. Therefore, the football is in the air for approximately 3.79 seconds.

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The football is in the air for 2.75 seconds.

The given function h = -4(4t-11) models the height h of the ball t seconds after it is kicked. To find how long the football is in the air, we need to find the time when the ball reaches the ground. This occurs when the height h is equal to 0. So, we can set the equation -4(4t-11) = 0 and solve for t.

-4(4t-11) = 0

4t-11 = 0

4t = 11

t = 11/4

Hence, the football is in the air for 11/4 seconds or 2.75 seconds.

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Answer:

As a fraction: [tex]y=\frac{56}{5}[/tex]

As a decimal: [tex]y=11.2[/tex]

As an ordered pair: [tex](0,\frac{56}{5} )[/tex] or [tex](0,11.2)[/tex]

Step-by-step explanation:

First we are using the slope formula to find the equation of our line:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where

[tex]m[/tex] is the slope of the line

[tex](x_1,y_1)[/tex] are the coordinates of the first point

[tex](x_2,y_2)[/tex] are the coordinates of the second point

our first point is (8, 0) and our second point is (3, 7), so [tex]x_1=8[/tex], [tex]y_1=0[/tex], [tex]x_2=3[/tex], and [tex]y_2=7[/tex].

Replacing values:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-0}{3-8}[/tex]

[tex]m=\frac{7}{-5}[/tex]

[tex]m=-\frac{7}{5}[/tex]

Now, to complete the equation of our line (and find its y-intercept), we are using the point slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

Where

[tex]m[/tex] is the slope

[tex](x_1,y_1)[/tex] are the coordinates of the first point

Replacing values:

[tex]y-0=-\frac{7}{5} (x-8)[/tex]

[tex]y=-\frac{7}{5} x+\frac{56}{5}[/tex]

Now, in a line of the form [tex]y=mx+b[/tex], [tex]b[/tex] is the way intercept. We can infer form our line that [tex]b=\frac{56}{5}[/tex], so the y-intercept of the line joining the points (8, 0) and (3, 7) is [tex]\frac{56}{5}[/tex].

Answer:

-2040

Step-by-step explanation:

[tex]S_n=a_1\dfrac{r^n-1}{r-1} \qquad\text{for first term $a_1$ and common ratio r}\\\\S_8=-8\dfrac{2^8-1}{2-1}=-2040[/tex]

The sum of the first 8 terms is -2040.

Answer:

Step-by-step explanation:

Euler's formula is

V - E + F = 2

Givens

V = 15

E = 15

F = ?

Solution

15 - 15 + F = 2

F = 2

I'm not sure this makes sense, but it is what the formula gives you.

The student can calculate the number of edges in a polyhedron by using Euler's formula for polyhedra. Given the number of faces and vertices, both being 15, we solve for edges and find that the polyhedron would have 28 edges.

The student wants to calculate the missing number of edges in a geometrical shape given the number of faces and vertices. This can be solved in mathematics using Euler's formula for polyhedra which is Faces + Vertices - Edges = 2. In the current situation, where the shape has 15 faces and 15 vertices, you can solve for edges. Inserting these values into Euler's equation yields: 15 (faces) + 15 (vertices) - Edges = 2. As a result, Edges = 15 + 15 - 2 = 28 edges.

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Answer:

We can use this knowledge in planning of cities

Step-by-step explanation:

The transversal is a line that intersects two or more parallel lines.Angles with similar characteristics are formed when this occurs.

In city planning, streets can be designed to resemble parallel lines with roads that do not meet.However, other roads can be constructed to allow people on the other street to cross to neighboring streets.Such roads allowing this access can be viewed as transversal.

The areas where street roads meet the transversal roads have similar angle characteristics thus could be used for CCTV cameras for surveillance and traffic lights positioning.

Answer:

Between A and B : Decreasing

Between B and C : Increasing

Between C and D : Decreasing

Between D and E : Constant

Step-by-step explanation:

If graph goes downward between two points then it indicates function is decreasing.

If graph goes upward between two points then it indicates function is increasing.

If graph goes parallel to the x-axis between two points then it indicates function is constant.

Then final answer is given by:

Between A and B : Decreasing

Between B and C : Increasing

Between C and D : Decreasing

Between D and E : Constant

Answer:

Step-by-step explanation:

f(x) + n - translation n units up

f(x) - n - translation n units down

f(x + n) - translation n units to the left

f(x - n) - translation n units to the right

===========================================

g(x) = 21

translation 7 units down: g(x) - 7 = 21 - 7 = 14

Moving a graph or function vertically down is as simple as subtracting the number of units you wish to move from the original function. The function g(x) = 21 moved 7 units down resulting in h(x) = 14.

A vertical translation in a graph is a shift in the graph either up or down along the y-axis. In the case of the function g(x) = 21, which is a horizontal line at y = 21, a vertical translation 7 units down would yield the new function h(x) = 21 - 7 = 14. Therefore, the equation that represents this translation is h(x) = 14.

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Answer:

99.87% of cans have less than 362 grams of lemonade mix

Step-by-step explanation:

Let the the random variable X denote the amounts of lemonade mix in cans of lemonade mix . The X is normally distributed with a mean of 350 and a standard deviation of 4. We are required to determine the percent of cans that have less than 362 grams of lemonade mix;

We first determine the probability that the amounts of lemonade mix in a can is less than 362 grams;

Pr(X<362)

We calculate the z-score by standardizing the random variable X;

Pr(X<362) = [tex]Pr(Z<\frac{362-350}{4})=Pr(Z<3)[/tex]

This probability is equivalent to the area to the left of 3 in a standard normal curve. From the standard normal tables;

Pr(Z<3) = 0.9987

Therefore, 99.87% of cans have less than 362 grams of lemonade mix

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\(y-3)^2=4y-12\\\\(y-3)^2=4(y-3)\\\\(y-3)(y-3)=4(y-3)\iff y-3=0\ \vee\ y-3=4\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}\\\\y-3=4\qquad\text{add 3 to both sides}\\\boxed{y=7}[/tex]

[tex]\bold{METHOD\ 2}\\\\(y-3)^2=4y-12\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\y^2-2(y)(3)+3^2=4y-12\\\\y^2-6y+9=4y-12\qquad\text{subtract}\ 4y\ \text{from both sides}\\\\y^2-10y+9=-12\qquad\text{add 12 to both sides}\\\\y^2-10y+21=0\\\\y^2-3y-7y+21=0\\\\y(y-3)-7(y-3)=0\\\\(y-3)(y-7)=0\iff y-3=0\ \vee\ y-7=0\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}\\\\y-7=0\qquad\text{add 7 to both sides}\\\boxed{y=7}[/tex]