Mark the points with the coordinates (4, 14), (22, 6), and (16, 18). Connect the points to form a triangle.

The equation that reveals the minimum value for the equation is 2(x + 3)² = 32

Which reveals the minimum value for the equation

From the question, we have the following parameters that can be used in our computation:

2x² + 12x − 14 = 0

Rewrite as

2x² + 12x = 14

So, we have

2(x² + 6x) = 14

Take the coefficient of x

k = 6

Divide by 2

k/2 = 3

Square both sides

(k/2)² = 9

So, we have

2(x² + 6x + 9) = 14 + 2 * 9

2(x² + 6x + 9) = 32

Express as squares

2(x + 3)² = 32

Hence, the equation that reveals the minimum value for the equation is 2(x + 3)² = 32

Question

Which of the following reveals the minimum value for the equation 2x^2 + 12x - 14 = 0?

2(x + 6)^2 = 26

2(x + 6)^2 = 20

2(x + 3)^2 = 32

Answer:

x=[tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

4x-6=10x-3 (add 6 to both sides)

4x=10x+3 (subtract 10x from both sides)

-6x=3 (divide both sides by -6)

x=[tex]\frac{-1}{2}[/tex]

Answer: X = -1/2

Step-by-step explanation: Your goal is to isolate x. First, subtract 4x from each side.

-6 = 6x - 3

Add 3 on both sides.

-3 = 6x

Divide by 6 on each side.

X = -1/2

Answer:

(1, 1 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 5 → (1)

3x + 2y = 5 → (2)

We can eliminate the term in x by multiplying (1) by 3 and (2) by - 2

6x + 9y = 15 → (3)

- 6x - 4y = - 10 → (4)

Add (3) and (4) term by term

(6x - 6x) + (9y - 4y) = (15 - 10), that is

5y = 5 ( divide both sides by 5 )

y = 1

Substitute y = 1 in either (1) or (2) and solve for x

Substituting in (1), then

2x + (3 × 1) = 5

2x + 3 = 5 ( subtract 3 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Solution is (1, 1 )

Answer:

C. [tex]y=(x-3)^2[/tex] and [tex]y=x^2-6x+9[/tex]

Step-by-step explanation:

before answering the problem let us remind the formula for square of sum and differences

[tex](a+b)^2=a^2+2 \times a \times b + b^2[/tex]

[tex](a-b)^2=a^2-2 \times a \times b + b^2[/tex]

We are going to use the above two formulas to solve each part and come to an answer

A. [tex]y = (x + 3)^2[/tex]

[tex](x + 3)^2=x^2+2 \times x \times 3 + 3^2[/tex]

[tex](x + 3)^2=x^2+6x+9[/tex]

Hence this option is not correct pair

B. [tex]y = (x-5)^2[/tex]

[tex](x - 5)^2=x^2-2 \times x \times 5 + 5^2[/tex]

[tex](x -5)^2=x^2-10x+25[/tex]

Hence this option is also not correct pair

C. [tex]y = (x -3)^2[/tex]

[tex](x - 3)^2=x^2-2 \times x \times 3 + 3^2[/tex]

[tex](x -3)^2=x^2-6x+9[/tex]

Hence this option is correct as it have equivalent pair

D. [tex]y = (x + 5)^2[/tex]

[tex](x + 5)^2=x^2+2 \times x \times 5 + 5^2[/tex]

[tex](x + 5)^2=x^2+10x+25[/tex]

Hence this option is also not correct pair

It is not A. because 8 is not a prime number.

It is not B. because 12 is not a prime number.

C. 2 x 2 x 2 x 2 x 2 x 3 = 4*4*6= 96

D. 2 x 2 x 2 x 2 x 2 x 3 x 3= 4*4*6*3=16*18= 288

Answer is C. -2 x 2 x 2 x 2 x 2 x 3 : 96 ( not D. = 298 , 298 is greater than 96)

The prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.

A number can be expressed as a product of its prime factors through the process of prime factorization. Prime factorization is the process of factorizing the bigger numbers in a way that all the numbers are prime.

Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is any natural number greater than one that is not prime.

The given number is 96. The factorization of the number 96 will be done as below:-

96 = 2 x 2 x 2 x 2 x 2 x 3

Therefore, the prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.

To know more about prime factorization follow

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Answer:

Option C: (x − 3)(x + 3)(2x + 1)

Step-by-step explanation:

Step-by-step explanation:

Draw a picture (like the image below).

Notice that triangles ABC and ACD both contain right angles, and both contain angle A (20°).  Since angles of a triangle add up to 180°, that means their third angle must also be the same (70°).

Also notice that triangles ABC and CBD both contain right angles, and both contain angle B (70°).  So their third angle must also be the same (20°).

Therefore:

m∠CDB = 90°

m∠CBD = 70°

m∠BCD = 20°

m∠CDA = 90°

m∠CAD = 20°

m∠ACD = 70°

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Actually, you have not "given" the domain.

The domain of F(x)=x^2+2 is "the set of all real numbers," because F(x)=x^2+2 is a polynomial.

F(x^2) = (x^2) + 2 = x^4 + 2.  Again, this is a polynomial and the domain is "the set of all real numbers."

Double check to ensure that you have copied down this problem correctly.

Answer:

C, E, F

Step-by-step explanation:

The range of the function [tex]g(x)=x^2[/tex] is [tex]y\in [0,\infty)[/tex], the range of the function [tex]h(x)=-x^2[/tex] is [tex](-\infty,0][/tex]

This means that for any value of x, the value of [tex]g(x)[/tex] is always greater or equal to the value of [tex]h(x)[/tex] (the values are equal at x=0).

So, options A and B are false, because at x=0 the values are equal and h(x) cannot be greater than g(x)

Options C, E and F are true, because for all non-zero x, g(x)>h(x).

Option D is false (the reason is the same as for option B)

Answer:

s(x) = f(x) + g(x) = (5x + 2) + (7x + 4) = 12x + 6

p(x) = 6*g(x) = 6(7x + 4) = 42x + 24

Step-by-step explanation:

so the price difference is 19500 - 16770 = 2730.

if we take 19500 to be the 100%, what is 2730 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 19500&100\\ 2730&x \end{array}\implies \cfrac{19500}{2730}=\cfrac{100}{x}\implies \cfrac{50}{7}=\cfrac{100}{x}\implies 50x=700 \\\\\\ x=\cfrac{700}{50}\implies x=14[/tex]

Answer:

The answer is 14%

Step-by-step explanation:

1) Divide 19500 by 16770

16770/19500= 0.86

2) Multiply by 100 (this is the percentage between the original and find prices of the car)

0.86(100)= 86%

3) Subtract 86% from 100% to find the change in percentage

100-86= 14%

Therefore, the percentage decrease of the price of the car is 14%.

Hope this helps!

Answer:

A. 3x^2+19x-14

Step-by-step explanation:

Applying the distributive property the given expression is equal to 3x²+19x-14 (Letter A).

The properties of multiplication are:

For evaluating the given question, you should apply the distributive property.

The question gives the expression (x+7)(3x-2). Thus, from the distributive property, you have:

3x²-2x+21x-14

3x²+19x-14

From the given options of the question, 3x²+19x-14 is shown in option A.

Read more about the distributive property  here:

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Answer:

87.88 ft^2.

Step-by-step explanation:

Area = 1/2 * base * height

= 1/2 * 16.9 * 10.4

= 87.88 ft^2.

Answer:

87.88 ft²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 16. 9 and h = 10.4, so

A = 0.5 × 16.9 × 10.4 = 87.88 ft²

The answer is:

The fraction is equivalent to 80%.

To solve the problem, we need to remember that if we want to convert from numbers to percentual values, we need to multiply the given number by 100.

So, if we have the fraction four-fifths which is:

[tex]\frac{4}{5}=0.8[/tex]

If we need to convert it to percent, we need to multiply it by 100:

[tex]0.8*100=80(percent)[/tex]

Hence, we have that the fraction is equivalent to 80%.

Have a nice day!

Answer:

80%

Step-by-step explanation:

We know 4/5 is the same as 4 divided by 5 then using long division for 4 divided by 5 gives us 0.8 converting our number to a percent

0.8 x 100 = 80%

Answer: 14 gallons of gas.

Step-by-step explanation: For the fractions, find a common denominator, which would be 10. To get 1/5 to have a denominator of 10, multiply each number by 2. You would get 2/10. 7 gallons fills his tank from 2/10 to 7/10. Subtract the two fractions.

7/10 - 2/10 = 5/10.

7 gallons filled his tank half way. We are trying to find the amount to fill his tank all the way. So multiply 7 by 2.

7 x 2 = 14

14 gallons of gas will fill his tank all the way.

I hope this helps!

Ivan's gas tank can hold 17.5 gallons when full after being 1/5 full and then adding 7 gallons.

The total capacity of Ivan's gas tank:

Answer:

14, 18, 20, and 24 are not perfect squares.

The numbers that are not perfect squares are:

1. 20

2. 18

3. 14

4. 24

These numbers do not have integer square roots, which means they are not perfect squares.

A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 25 is a perfect square because [tex]\(5 \times 5 = 25\).[/tex]

Let's examine each number:

1. 25 - This is a perfect square because  [tex]\(5 \times 5 = 25\).[/tex]

2. 20 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

3. 18 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

4. 36 - This is a perfect square because [tex]\(6 \times 6 = 36\).[/tex]

5. 16 - This is a perfect square because [tex]\(4 \times 4 = 16\).[/tex]

6. 14 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

7. 24 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.

Therefore, the numbers that are not perfect squares are 20, 18, 14, and 24. They cannot be represented as the square of an integer. The other numbers, 25, 36, and 16, are perfect squares as they can be expressed as the square of an integer.

The complete question is here.

Which numbers are not perfect squares? 25 20 18 36 16 14 24

Step-by-step explanation:

exponential decay functions are written in the form :

[tex]y=ab^{x}[/tex]

where b is less than 1

if we look at the 3rd choice and consider the term on the right.

[tex](8/7)^{-x}[/tex]

= [tex](7/8)^{x}[/tex]

If we compare this to the general form above,

b = 7/8 (which is less than 1)

hence the 3rd choice is correct.

The function which is an exponential decay function is:

                       [tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]

We know that an exponential  function is in the form of:

          [tex]f(x)=ab^x[/tex]

where a>0 and  if 0<b<1 then the function is a exponential decay function.

and if b>1 then the function is a exponential growth function.

a)

[tex]f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x[/tex]

Here

[tex]b=\dfrac{7}{4}>1[/tex]

Hence, the function is a exponential growth function.

b)

[tex]f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}[/tex]

We know that:

[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]

Hence, we have the function f(x) as:

[tex]f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x[/tex]

Here

[tex]b=\dfrac{5}{4}>1[/tex]

Hence, the function is a exponential growth function.

c)

[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]

We know that:

[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]

Hence, we have the function f(x) as:

[tex]f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x[/tex]

Here

[tex]b=\dfrac{7}{8}<1[/tex]

Hence, the function is a exponential decay function.

d)

[tex]f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x[/tex]

Here

[tex]b=\dfrac{9}{2}>1[/tex]

Hence, the function is a exponential growth function.

Answer:

[tex]y+6=m(x+2)[/tex]

where I would have to look at the table to know [tex]m[/tex].

Step-by-step explanation:

Point-slope form of a line is

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

where [tex]m \text{ is the slope and } (x_1,y_1) \text{ is a point on that line}[/tex]

You are given [tex](x_1,y_1)=(-2,-6) \text{, but no value for }m[/tex].

So we know we are looking for an equation that looks like this:

[tex]y-(-6)=m(x-(-2))[/tex]

If you simplify this looks like:

[tex]y+6=m(x+2)[/tex]

Answer:

d

Step-by-step explanation:

Answer:

2.4 years

Step-by-step explanation:

you have to first convert the trees' heights into inches. three feet is equivalent to 36 inches and four feet is equivalent to 48 inches. Since three A grows at 15 inches a year it'll become a the expression 15x+36 and the expression for tree B will be 10x+48. You set them up to each other and simplify it.

15x+36=10x+48

 -10x        -10x

5x+36=48

   -36        -36

5x=12

/5    /5

x=2.4

So it'll be 2.4 years

[tex]\bf (\sqrt{5x+6})^2\implies \sqrt{(5x+6)^2}\implies 5x+6[/tex]

Answer:

[tex]c=7[/tex]

Step-by-step explanation:

They are just asking you to compare

[tex]ax^2+bx+c=0[/tex] to

[tex]3x^2+5x+7=0[/tex].

What constant values are in the place of [tex]a,b, \text{ and } c[/tex].

[tex]a=3[/tex]

[tex]b=5[/tex]

[tex]c=7[/tex]

Answer:

x=0

Step-by-step explanation:

(x-5)=4x-5

Subtract x from each side

x-5-x=4x-x-5

-5 = 3x-5

Add 5 to each side

-5+5 = 3x-5+5

0 = 3x

Divide by 3

0/3 = 3x/3

0 =x

x=0

Answer:

C 90

Step-by-step explanation:

Answer: OPTION B.

Step-by-step explanation:

You can observe in the figure provided that the angle 3 and the angle that measures 70° , share the same vertex, therefore, you can conclude that they are Vertical angles and they are congruent. Then:

[tex]m\angle 3=70\°[/tex]

You can notice that the angle 1 and the angle that measures 70° are Complementary angles (They add up to 90°), then you can find the measure of the angle 1:

[tex]m\angle 1+70\°=90\°\\\\m\angle 1=90\°-70\°\\\\m\angle 1=20\°[/tex]

Then:

[tex]m\angle 3-m\angle 1=70\°-20\°\\\\m\angle 3-m\angle 1=50\°[/tex]

Answer:

(3,2)

Step-by-step explanation:

We are given the system:

3x-y=7

2x-2y=2.

We are asked to solve this by substitution.  We need to pick an equation and pick a variable from that equation to solve for that variable.

I really like either for this.  Some people might go with the first one though. Let's do that.  I will solve the first one for y.

3x-y=7

Subtract 3x on both sides:

   -y=-3x+7

Divide both sides by -1:

     y=3x-7

Now we are ready for substitution.  We are going to plug this equation into the second equation giving us:

2x-2y=2 with y=3x-7 gives us:

2x-2(3x-7)=2

Distribute:

2x-6x+14=2

Combine like terms:

-4x+14=2

Subtract 14 on both sides:

-4x      =2-14

Simplify:

-4x       =-12

Divide both sides by -4:

  x       =-12/-4

Simplify:

 x         =3

So using y=3x-7 and x=3, I will find y now.

y=3x-7 if x=3

y=3(3)-7   (I inserted 3 for x since we had x=3)

y=9-7       (Simplified)

y=2           (Simplified)

The answer is (x,y)=(3,2).

Answer:

98.1% chance of being accepted

Step-by-step explanation:

Given:

sample size,n=56

acceptance condition= at most 2 batteries do not meet specifications

shipment size=7000

battery percentage in shipment that do not meet specification= 1%

Applying binomial distribution

In this formula, a is the acceptable number of defectives;

 n is the sample size; 

p is the fraction of defectives in the population.  

Now putting the value

a= 2

n=56

p=0.01

[tex]\frac{56!}{0!\left(56-0\right)!}\left(0.01\right)^0\:\left(1-0.01\right)^{\left(56-0\right)} + \frac{56!}{1!\left(56-1\right)!}\left(0.01\right)^1\:\left(1-0.01\right)^{\left(56-1\right)} +[/tex][tex]\:\frac{56!}{2!\left(56-2\right)!}\left(0.01\right)^2\:\left(1-0.01\right)^{\left(56-2\right)}[/tex]

=0.56960+0.32219+0.08949

After summation, we get 0.981 i.e. a 98.1% chance of being accepted.  As this is such a high chance, we can expect many of the shipments like this to be accepted!

Answer:

yes

Step-by-step explanation:

let me explain more in depth. 1: yes, it's the point where the function crosses the x axis. 2: the absence of acceleration. 3: I think it can be negative

If there was an illustration, I would be happy to assist you.

Let c be children and a adults.

3.5c + 7a = 1771 (the total revenue is equal to the amounts made off of people)

c + a = 331 (total number of people)

The second formula becomes a = 331 - c. This can be substituted into the first formula.

3.5c + 7(331 - c) = 1771 = 7*331 - 3.5c = 1771. 7*331 = 2317, so 3.5c = 2317 - 1771 = 546.

546/3.5 = 156 = c (number of children).

c + a = 156 + a = 331 => a = 331 - 156 = 175 (number of adults).

There are 156 children and 175 adults

Answer:

156 children

175 adults

Step-by-step explanation:

Let's call x the number of children admitted and call z the number of adults admitted.

Then we know that:

[tex]x + z = 331[/tex]

We also know that:

[tex]3.50x + 7z = 1,771.00[/tex]

We want to find the value of x and z. Then we solve the system of equations:

-Multiplay the first equation by -7 and add it to the second equation:

[tex]-7x - 7z = -2,317[/tex]

[tex]3.50x + 7z = 1,771[/tex]

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

[tex]-3.5x = -546[/tex]

[tex]x =\frac{-546}{-3.5}\\\\x=156[/tex]

Now we substitute the value of x in the first equation and solve for the variable z

[tex]156 + z = 331[/tex]

[tex]z = 331-156[/tex]

[tex]z = 175[/tex]