consider the function f(x)=15x^2+60-19 Part A: Write the function in vertex form. Part B: Name the vertex for the function

The last option is not even a function, because it ambiguously defines the endpoints.

The first option doesn't define the endpoint, because they are always excluded.

So, the correct option is the second one, because it includes the left endpoint and excludes the right one.

The function d(x) is given by:

d(x)=  1 if   1≤x<4

         2 if  4≤x<6

        3.5 if  6≤x<11

and  5  if 11≤x<13

                    1 when 1≤x<4

( because the graph is a straight horizontal line i.e. y=1 and the line has a closed circle at x=1 and open circle at x=4 )

( because the graph is a straight horizontal line i.e. y=2 and the line has a closed circle at x=4 and open circle at x=6 )

( because the graph is a straight horizontal line i.e. y=3.5 and the line has a closed circle at x=6 and open circle at x=11 )

( because the graph is a straight horizontal line i.e. y=5 and the line has a closed circle at x=11 and open circle at x=13 )

Answer: its B

Step-by-step explanation:

Answer:

7*-5=-35

so your answer would be D

If the dices have equal probability, that means each number has a 1/6 chance of getting picked because there are 6 sides to a dice with 6 different numbers.

There are a total of 36 combinations, because 6 * 6 is 36.

It would be impossible to have a sum of 1, as the lowest number on both dice is 1. 1 + 1 = 2. Therefore there is a 0/36 probability of getting a sum of 1.

See the attached picture:

ANSWER

[tex]f( - 1) = 0[/tex]

EXPLANATION

From the table the values of x, are on the left and the values of f(x) are on the right.

To find f(-1), we look for the value under f(x) that corresponds to x=-1.

This value is 0.

Therefore

[tex]f( - 1) = 0[/tex]

A function assigns the values. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

As per the given table the value of f(-1), or the value of f(x), when the value of x=-1, is 0. Thus, it can be written that the value of f(-1) is 0.

Hence, the correct option is C.

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Answer:

1/81

Step-by-step explanation:

Remember:

b^-n = 1/b^n

Then

[(3^2)]^-2 = 1/[9^2]

1/81

Best regards

Answer:

The correct answer option is [tex]\frac { 1 } { 81 } [/tex].

Step-by-step explanation:

We are given the following expression and we are to find out whether which of the given answer options is equivalent to this expression:

[tex] ( 3 ^ 2 ) ^ { - 2 } [/tex]

We know the rule for solving the exponents:

[tex] ( b ^ n ) ^ { m } = b ^ { n \cdot m} [/tex]

This means that the exponents are multiplied with each other.

So, if we multiply them, for the given expression we get:

[tex] ( 3 ) ^ { - 4 } [/tex] = [tex] \frac { 1 } { 3 ^ 4 } = \frac { 1 } { 81 } [/tex]

Given a quadratic equation [tex]ax^2+bx+c=0[/tex]

The discriminant is defined as

[tex]\Delta=b^2-4ac[/tex]

In your case, the equation is defined by the coefficients

[tex]a=3,b=0,c=-10[/tex]

So, the discriminant is

[tex]\Delta=0^2-4\cdot 3\cdot (-10) = 120[/tex]

The discriminant is involved in the solving formula as follows:

[tex]x_{1,2} = \dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]

Which implies that:

In your case, since the discriminant is positive, you have two distinct solutions. Since 120 is not a perfect square, however, you will not get rid of the square root, so you will have two distinct irrational solutions.

The equation 3x² - 10 = 0 has a discriminant of 120, which is greater than zero. This means that there are two distinct real roots for this equation.

To describe the roots of the equation 3x² - 10 = 0 using the discriminant, we must first understand that the discriminant (d) of a quadratic equation of the form ax² + bx + c = 0 is given by b2 - 4ac. For our equation, a = 3, b = 0, and c = -10, so the discriminant
would be:
= (0)2 - 4(3)(-10) = 0 + 120 = 120

Since  > 0, this indicates that there are two distinct real roots. When the discriminant is greater than zero, the quadratic equation has two real solutions. Therefore, in this case, 3x2 - 10 = 0 has two real roots, corresponding to the x-values where the parabola intersects the x-axis.

As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.

In order to solve for x we can set up the proportion between the horizontal and vertical sides:

[tex]28\div 11.2 = 27+x \div x[/tex]

Solving this proportion for x implies [tex]x=18[/tex]

Now you can solve for m and p using the pythagorean theorem, because both triangles are right:

[tex]m = \sqrt{18^2+11.2^2} =21.2[/tex]

Then, we know that the hypothenuse of the big triangle is m+p, so we have

[tex]m+p=\sqrt{(18+27)^2+28^2} = 53[/tex]

which implies

[tex]p = 53-p = 53-21.2=31.8[/tex]

The ratio of the given to similar triangles is 0.4. value of the x, m, and p is 18, 21.2, and 31.8.

Similar triangles are triangles whose corresponding sides are in ratio, while the corresponding angles are of equal measure.

As the two sides of the triangles are already given, therefore, the ratio of these two triangles are,

[tex]\dfrac{11.2}{28} = \dfrac{2}{5}[/tex]

As we already know the ratio of the two triangles, therefore,

[tex]\dfrac{x}{27+x} = \dfrac{2}{5}\\\\5x = 54 + 2x\\\\5x-2x = 54\\\\3x = 54\\\\x = 18[/tex]

Hence, the value of x is 18.

As the given triangle is a right-angled triangle, therefore, we can use the Pythagorean theorem to find the value of m,

[tex](Hypotenuse)^2 = (Perpendicular)^2+(Base)^2\\\\m^2 = x^2 + (11.2)^2\\\\m^2 = 18^2 + 11.2^2\\\\m^2 = 324+125.44\\\\m^2 = 449.44\\\\m = 21.2[/tex]

Thus, the value of side m is 21.2 units.

The value of m and p can be found using the same ratio, we already have for similar triangles,

[tex]\dfrac{m}{m+p} = \dfrac{2}{5}\\\\\dfrac{21.2}{21.2+p} = \dfrac{2}{5}\\\\106= 42.4 + 2p\\\\p = 31.8[/tex]

Thus, the value of the x, m, and p is 18, 21.2, and 31.8.

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The formula for lateral surface of a cylinder is:

SA = 2 *PI * r *h

Replace the letters with the given values:

400 = 2 * PI * r *40

Multiply the right side:

400 = r * 251.2

Divide both sides by 251.2:

r = 400 / 251.2

r = 1.59

The radius is 1.59 inches.

Answer: 1.59

Step-by-step explanation:

5 and 6

because 5 squared is 25 and 6 squared is 36 so 29 is in between

Answer:

A, C

Step-by-step explanation:

I had answered this earlier, so you better look back at that question.

To reiterate, use the Pythagorean Theorem a^2+b^2=c^2.

If a^2+b^2=c^2, it is a right triangle.

*remember that squaring a square root results in just the number inside the square root.

Answer:

12

Step-by-step explanation:

We are given first five multiples of 4 and 6 as shown below and we are to find their least common multiple.

Multiples of 4: 4, 8, 12, 16, 20, . . .

Multiples of 6: 6, 12, 18, 24, 30, . . .

From the given multiples, we can see that the number 12 and 24 are the common multiples which means that these numbers are multiples of both 4 and 6.

So the least common multiple will be 12.

The least common multiple (LCM) of 4 and 6 is 12. This is the smallest multiple that both numbers share.

The least common multiple (LCM) of two numbers is the smallest number that is evenly divisible by both of those numbers. In this case, we are looking for the LCM of 4 and 6.

To find the LCM, we can list the multiples of both numbers and look for the smallest common multiple.

Multiples of 4: 4, 8, 12, 16, 20, ...

Multiples of 6: 6, 12, 18, 24, 30, ...

From the lists, we can see that 12 is the smallest number that appears in both lists. Therefore, the LCM of 4 and 6 is 12.

So, the correct answer is 12. The LCM of 4 and 6 is 12 because it is the smallest number that is evenly divisible by both 4 and 6, as it appears in the list of multiples for both numbers.

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Answer:

Step-by-step explanation:

To find the indicated product, multiply each element in the 2x2 matrix by 3:

3(-6)     3(-11)

3(-14)     3(-8)

which comes out to:

-18         -33

-42         -24

This corresponds to the 2nd answer choice.

Answer: OPTION D

Step-by-step explanation:

THe quadratic formula is shown below:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

Given the quadratic equation shown in the image, you have that:

a=1

b=3

c=4

Therefore, when you susbtityte these values into the formula you obtain the following solution:

[tex]x=\frac{-3\±\sqrt{3^2-4(1)(4)}}{2*1}[/tex]

[tex]x=\frac{-3\±\sqrt{-7}}{2}[/tex]

Answer:

D.x = (-3±√-7) / 2

Step-by-step explanation:

We have given  a quadratic equation.

x²+3x+4  = 0

From above equation, a = 1, b = 3 and c = 4

We have to find the solution of given equation bu using quadratic formula.

x  = (-b±√b²-4ac) / 2a

Putting given values in above formula, we have

x = (-3±√(3)²-4(1)(4) ) / 2(1)

x = (-3±√9-16) / 2

x = (-3±√-7) / 2 which is the answer.

The cost at which both video rental plans are the same is $48, which occurs when a customer borrows 20 DVDs in a month.

The student asked about the cost at which both video rental plans offered by a company would be equal in value. To find this, we need to establish an equation for each plan and set them equal to each other. The first plan includes a membership fee of $8 and charges $2 for every DVD borrowed, which can be represented as cost = $2 × number of DVDs + $8. The second plan is a flat rate of $48 per month for unlimited rentals.

Now we set the equations equal to each other: $2 × number of DVDs + $8 = $48. Solving for the number of DVDs would look like this:

Therefore, the break-even point where both plans cost the same amount is at 20 DVDs borrowed. At this point, the customer would pay $48 with either plan.

Answer:

The point of intersection is

(7,-2)

Step-by-step explanation:

We can easily solve this equation by plotting each graph in a graphing tool or calculator.

If we do this, we can find the intersection between the three lines and prove that it exists.

We are solving the system of equations

x+y=5

2x–y=16

x+2y=3

Please see attached picture.

The point of intersection is

(7,-2)

Answer:

The answer is 1/9.

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Hope this helps. :D

For this case we have that by definition, any number raised to zero results in "1".

That is to say:

[tex]a ^ 0 = 1[/tex]

Then, given the following expression:

[tex]\frac {(- 3) ^ 0} {(- 3) ^ 2} = \frac {1} {(- 3) (- 3)} =[/tex]

Taking into account that:

[tex]- * - = +\\\frac {1} {(- 3) (- 3)} = \frac {1} {9}[/tex]

Answer:

[tex]\frac {1} {(- 3) (- 3)} = \frac {1} {9}[/tex]

Option c

Answer:

B. 3/5

Step-by-step explanation

1/5 of icing = 1/3 of a cake

1/3 * 3/1 = 3/3 = 1 (a whole cake)

1/5 * 3/1 = 3/5

The answer to your question is B, 3/5.

Slower bike = X

Faster bike = X+9

They both ride for 2 hours, now you have 2x and 2(x+9)

The sum of the two cyclists is 66 miles:

2x +2(x+9) = 66

Use distributive property:

2x + 2x+18 = 66

Simplify:

4x +18 = 66

Subtract 18 from both sides:

4x = 48

Divide both sides by 4:

x = 48/4

x = 12

The slower bike was going 12 mi/h

The faster bike was 12+9 = 21 mi/h.

Answer:

Step-by-step explanation:

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

We have:

[tex]b_1=12,\ b_2=5,\ h=5[/tex]

Substitute:

[tex]A=\dfrac{12+5}{2}\cdot5=\dfrac{17}{2}\cdot5=8.5\cdot5=42.5[/tex]

Answer:

The numbers are

14

and

7

.

Explanation:

Let the numbers be

x

and

y

.

x

+

y

=

21

x

−

y

=

7

y

=

21

−

x

x

−

(

21

−

x

)

=

7

x

−

21

+

x

=

7

2

x

=

28

x

=

14

∴

14

+

y

=

21

y

=

7

Answer:  The required numbers are 14 and 7.

Step-by-step explanation:  Given that the sum of two numbers is 21 and their difference is 7.

We are to find the numbers.

Let x and y represents the two numbers.

Then, according to the given information, we have

[tex]x+y=21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Adding equations (i) and (ii), we get

[tex](x+y)+(x-y)=21+7\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.[/tex]

From equation (i), we get

[tex]x+y=21\\\\\Rightarrow 14+y=21\\\\\Rightarrow y=21-14\\\\\Rightarrow y=7.[/tex]

Thus, the required numbers are 14 and 7.

Answer:

24 x + 10 y >= 200

Step-by-step explanation:

as x represents centerpiece and y represent  bouquet and total number of roses should be atleast 200 which means we can use roses more than 200 but not less than 200,  the equation will be:

24 x + 10 y >= 200

Answer:

[tex]24x+10y\geq 200[/tex]

Step-by-step explanation:

Givens:

According to the problem, we can define the number of roses per a centerpiece: [tex]24x[/tex]

The number of roses per bouquet: [tex]10y[/tex]

So, the problem restricts the amount of roses, at least 200, that means, 200 or more than 200 roses. Therefore the expression that represent the amount of roses would be:

[tex]24x+10y\geq 200[/tex]

As you can observe, the inequality includes the 200 roses restriction, and the amount of roses per centerpieces and per bouquet.

Answer:

x= -2,-3

Step-by-step explanation:

Answer:

28 in

Step-by-step explanation:

6+2= 8 so therefore the length is eight.

To find perimeter, add up all the sides of the rectangle so 6+6+8+8=28

Final answer:

The perimeter of the rectangle is calculated using its length and width. With a width of 6 inches and 2 inches added to determine the length, the perimeter is found to be 28 inches.

Explanation:

To determine the perimeter of the rectangle, we first have to calculate both the width and the length. The width is given as 6 inches. The problem states that the length is 2 inches more than its width, which means the length is 6 inches + 2 inches = 8 inches.

The formula to compute the perimeter (P) of a rectangle is P = 2 * (length + width). Substituting our values, we get P = 2 * (8 inches + 6 inches) = 2 * 14 inches = 28 inches. Therefore, the perimeter of the rectangle is 28 inches.

Y=1000(1+00.6) so divide y by 92 and get 1

Answer:

y=6x+100

Step-by-step explanation:

im not 100% sure if this is correct but i used an online graphing calculator!

A power of 10 is the number 10 multiplied by itself by the number of times indicated by the exponent. Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000.

1/100,000,000 expressed as a power of 10 is 10-8, reflecting the movement of the decimal point 8 times to the left.

The question asks for the expression of 1/100,000,000 as a power of 10. To find the answer, we need to realize that this fraction is the same as moving the decimal point 8 places to the left from 1, making it 0.00000001. This operation is equivalent to the negative power of 10, because you're making the number smaller (or dividing). Remembering that the exponent represents how many times we move the decimal place, we can express 1/100,000,000 as 10-8.

Answer:

y = x²/4 + x/2 + 21/4 ⇒ -9 ≤ x ≤ 7

Step-by-step explanation:

∵ x = 2t - 1

∴ 2t = x + 1 ⇒ t = (x + 1)/2

∵ y = t² + 5

∴ y = [(x + 1)/2]² + 5 = (x² + 2x + 1)/4 + 5

  y = x²/4 + x/2 + 1/4 + 5 = x²/4 + x/2 + 21/4

∵ -4 ≤ t ≤ 4

∴ -9 ≤ x ≤ 7

Answer:

a: 162 ft^2

Step-by-step explanation:

Lets turn the inches into feet. Every one inch is 3 feet so 3 inches is 9 feet and 6 inches is 18 feet. 9*18=162. The area of the playground is 162 ft^2

Answer:

120

Step-by-step explanation:

Using the definition

n[tex]P_{r}[/tex] = n! / (n - r ) !

where n! = n(n - 1)(n - 2) ....... × 3 × 2 × 1

Hence

5[tex]P_{5}[/tex] = 5! / 0! = 5! ← 0! = 1

5[tex]P_{5}[/tex] = 5! = 5 × 4 × 3 × 2 × 1 = 120

In mathematics, the permutation '5P5' equals 1 because there is exactly one way to arrange 5 items in 5 spots.

The problem you are asked to solve involves understanding permutations, which in mathematics, is a way to calculate the number of possible arrangements of a set of items. Specifically, the permutation you are asked to evaluate is written as '5P5'.

In permutation notation, the expression 'nPn' always equals 1, because there are exactly 1 ways you can arrange 'n' items in 'n' spots.

Therefore, the solution to '5P5' is 1.

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Answer:

The area of the rectangle is 2/15

Step-by-step explanation:

To figure this out you have to multiply the length and the width

2/5×1/3 = 2/15

This is the simplified answer