Determine the vertex of the graph of the following parabola. f(x)=−(x−2)2−3

Using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.

An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.

The arity of the operation is influenced by the number of operands.

PEMDAS, parenthesis, exponents, multiplication, and division.

So, the value of x will be:

The given two rectangles have similar sides.

2cm is similar to 4cm.

3cm is similar to xcm.

Now, we can calculate x as follows:

2/4 = 3/x

2x = 4×3

2x = 12

x = 12/x

x = 6

Therefore, using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.

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The equation of the line that has a slope of -2 and x-intercept of -1 in point slope form is y = -2(x + 1).

Linear equations can be represented in different form such as point slope form, slope intercept form, general form and standard form.

Therefore, let's represent the equation of the line in point slope form.

Using point slope form,

y - y₁ = m(x - x₁)

where

Therefore, the equation of the line has a slope of -2 and an x-intercept of -1.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.

hence,

m = -2 and (-1, 0)

x₁ = -1

y₁ = 0

Therefore,

y - 0 = -2(x + 1)

y = -2(x + 1)

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Answer:

6

Step-by-step explanation:

The cardinal number of a finite set is the number of elements of the set.

cardinal number = 6

Answer:

wean positive realtionship

Answer:

B

Step-by-step explanation:

Since -1 is greater the values given then x is less than -1

Answer:

7

Step-by-step explanation:

THe answer is 7 because 10-3=7 SOrry if wrong

From the given figure

a) The value of y = 6

b) The length of the line RS = 39 units

The length of the line ST = 38 units

The length of the line RS = 6y + 3

The length of the line ST = 5y + 8

The length of the line RT = 77

From the line we can say that

RT = RS + ST

77 = 6y + 3 + 5y + 8

Add the like terms

11y + 11 = 77

11y = 77 - 11

11y = 66

y = 66/11

y = 6

The value of y = 6

The length of RS = 6y + 3

= 6×6 + 3

= 36 + 3

= 39 units

The length of the line ST = 5y + 8

= 5×6 + 8

= 30 + 8

= 38 units

Hence, from the given figure

a) The value of y = 6

b) The length of the line RS = 39 units

The length of the line ST = 38 units

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Answer:

B

Step-by-step explanation:

3([tex]3^{2}[/tex]) + 2([tex]8^{2}[/tex])

3(9) + 2(64)

27 + 128

155

A statement of given information can be used in a two column proof

The two-column proof is summarized in the statement and reason columns, and each statement must have a verified reason. Two-column proof reasons are usually given information, vocabulary definitions, hypotheses, and previously proven theorems.

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Step-by-step explanation:

Let us identify which quadratic function is positive. Yeah, let's start.

Y = [tex]{ \red{ \sf{2 {x}^{2} - 17x + 30}}}[/tex]

By using factorisation method,

[tex]{ \red{ \sf{2 {x}^{2} - 12x - 5x + 30}}}[/tex]

Take common factors

[tex]{ \red{ \sf{2x(x - 6) - 5(x - 6)}}}[/tex]

[tex]{ \red{ \sf{(2x - 5)}}} \: \: \: \: \: \: \: || \: \: \: \: \: { \red{ \sf{(x - 6)}}}[/tex]

[tex]{ \red{ \sf{2x - 5 = 0}}} \: \: || \: \: { \red{ \sf{x - 6 = 0}}}[/tex]

[tex]{ \red{ \sf{2x = 5}}} \: \: \: \: \: \: \: \: \: || \: \: \: \: { \red{ \boxed{ \green{ \sf{x = 6}}}}}[/tex]

[tex]{ \red{ \sf{{ \frac{ \cancel2}{ \cancel2}x}}}} = { \red{ \sf{ \frac{5}{2}}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{5}{2}}}}}} [/tex]

____________________________________

Y = [tex]{ \blue{ \sf {{ - x}^{2} - 6x - 8}}}[/tex]

By using factorisation method,

[tex]{ \blue{ \sf{ - {x}^{2} - 2x - 4x - 8}}}[/tex]

Take common factors

[tex]{ \blue{ \sf{ - x(x + 2) - 4(x + 2)}}}[/tex]

[tex]{ \blue{ \sf{( - x - 4)}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{(x + 2)}}}[/tex]

[tex]{ \blue{ \sf{- x - 4 = 0}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{x + 2 = 0}}}[/tex]

[tex]{ \blue{ \boxed{ \green{ \sf{x = -4}}}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]

Hence, the first quadratic function is positive and second quadratic function is negative.

Answer:

[tex]\textsf{$y = 2x^2 - 17x + 30$: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}[/tex]

[tex]\textsf{$y = - x^2 - 6x - 8$: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}[/tex]

Step-by-step explanation:

A function is positive when it is above the x-axis, and negative when it is below the x-axis.

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Given quadratic equation:

[tex]y = 2x^2 - 17x + 30[/tex]

Factor the equation:

[tex]\implies y = 2x^2 - 17x + 30[/tex]

[tex]\implies y = 2x^2 - 5x-12x + 30[/tex]

[tex]\implies y=x(2x-5)-6(2x-5)[/tex]

[tex]\implies y=(x-6)(2x-5)[/tex]

The x-intercepts of the parabola are when y = 0.

To find the x-intercepts, set each factor equal to zero and solve for x:

[tex]\implies x-6=0 \implies x=6[/tex]

[tex]\implies 2x-5=0 \implies x=\dfrac{5}{2}[/tex]

Therefore, the x-intercepts are x = ⁵/₂ and x = 6.

The leading coefficient of the given function is positive, so the parabola opens upwards.  

The function is positive when it is above the x-axis.

Therefore, the function is positive for the values of x less than the smallest x-intercept and more than the largest x-intercept:

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Given quadratic equation:

[tex]y = - x^2 - 6x - 8[/tex]

Factor the equation:

[tex]\implies y = - x^2 - 6x - 8[/tex]

[tex]\implies y = -(x^2 +6x +8)[/tex]

[tex]\implies y = -(x^2 +4x +2x+8)[/tex]

[tex]\implies y = -((x(x+4)+2(x+4))[/tex]

[tex]\implies y = -(x+4)(x+2)[/tex]

The x-intercepts of the parabola are when y = 0.

To find the x-intercepts, set each factor equal to zero and solve for x:

[tex]\implies x+4=0 \implies x=-4[/tex]

[tex]\implies x+2=0 \implies x=-2[/tex]

Therefore, the x-intercepts are x = -4 and x = -2.

The leading coefficient of the given function is negative, so the parabola opens downwards.  

The function is negative when it is below the x-axis.

Therefore, the function is negative for the values of x less than the smallest x-intercept and more than the largest x-intercept:

By taking a quotient between the lengths, we will see that 98 pieces of 1/4 foot can be made.

We know that the total length of the rope is (24 + 1/2) ft, to see how many pieces of 1/4 feet we can take from that rope, we need to take the quotient between the total length and the length of the pieces.

It gives:

Q = (24 + 1/2)ft/(1/4)ft = 4*(24 + 1/2)

Q = 4*24 + 4*(1/2)

Q = 96 + 4/2

Q = 96 + 2 = 98

So 98 pieces of 1/4 foot can be made.

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Answer:  

The area of the room is 34*21 = 714 ft^2

the cost of the carpet is $5 per square foot, so the cost to carpet the whole room will be

5*714 = $3570

Step-by-step explanation:

3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.

The area of Rectangle is length times of width.

Given that, Circular area rugs are priced at $5 per foot based on the circumference of the carpet used.

We need to find  the cost of the largest circular area rug that will fit in Susie’s dining room.

The area of the room is 34×21 = 714 ft²

The cost of the largest circular area rug that will fit in Susie’s dining room

$5 per foot based on the circumference of the carpet

Multiply 5 with 714

5×714

3570

Hence, 3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.

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Answer:

64

Step-by-step explanation:

Substitute the values so (3-2(-1/2))3

Then distribute so (3-(-1))3

Add since it's a double negative to get (4)3

And 4 cubed is 64

A. When x = -1, the value of y is equal to 3.

B. When y = 7, the value of x is equal to 1.

C. The y-intercept of the graph is equal to -2.5.

D. The x-intercept of the graph is equal to 5.

E. The slope of the line is equal to -1.75

F. The equation of the line is equal to y = -1.75x - 2.5

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Making slope (m) the subject of formula, we have the following:

Slope, m = (y - c)/x

Slope, m = (1 - (-2.5))/-2

Slope, m = (1 + 2.5)/-2

Slope, m = -3.5/2

Slope, m = -1.75.

For the equation of this line, we have:

y = mx + c

y = -1.75x - 2.5

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Answer:

Step-by-step explanation:

Answer:

nik

Step-by-step explanation:

(2,1) because if you graph it, the dot won’t be on the line.

Answer:

x = -3

y = 1

Step-by-step explanation:

Desmos is free and it will graph for you.  See picture.

The number 49 is a composite number because it has more than two factors.

A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.

Numbers with more than two factors are known as composite numbers. Non-prime numbers are composite numbers because they can be divided by more than two numbers.

A positive integer is a composite number. which is not the case (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes abbreviated as "composites") are 4, 6, 8, 9, 10, 12, 14, 15, and 16.

A composite number is one that can be formed by multiplying two smaller positive integers. It is a positive integer with at least one divisor other than 1 and itself. Every positive integer is either composite, prime, or the unit 1, so composite numbers are those that are neither prime nor a unit.

In this case, the factor of 49 are 1, 7 and 49. Therefore, it's a composite number.

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The percentage of lightbulb replacement requests numbering between 32 and 36 is 34

According to the question,

The distribution of the number of daily request is bell-shapes means Number of daily request follows Normal distribution

Mean of normal distribution : μ = 36

Standard deviation : σ = 4

Let the lightbulb replacement requests number be "x"

So, the probability of lightbulb replacement requests numbering between 32 and 36 = P(32 < x <36)

below 36 i.e. mean of normal

32 = 36 - 4 is probability between one standard deviation and below mean

Percentage between mean ± standard deviation is always 68%

so , percentage of lightbulb replacement requests numbering between 32 and 36 will be half of 68% as mean + standard deviation is excluded

= 68/2

= 34

Hence , 34 percentage of lightbulb replacement requests numbering between 32 and 36.

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Answer:

3 and 9

Step-by-step explanation:

x+y=12

y-x=6

y-x=6

 +x.  +x

y=6+x

x+(6+x)=12

6+2x=12

-6.    -6

2x=6

/2. /2

x=3

3+y=12

-3.  -3

y=9

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Answer:

an odd number

Step-by-step explanation:

it always will be an odd number when you add an even and an odd number

Answer:

[tex]f(x)=6(x-2)^2+18[/tex]

Step-by-step explanation:

Given quadratic function:

[tex]f(x)=6x^2-24x+42[/tex]

To complete the square, begin by grouping the x terms within parentheses:

[tex]\implies f(x)=(6x^2-24x)+42[/tex]

Factor out the coefficient of x²:

[tex]f(x)=6\left(x^2-4x\right)+42[/tex]

Add the square of half the coefficient of the term in x inside the parentheses, and subtract the distributed value outside the parentheses:

[tex]\implies f(x)=6\left(x^2-4x+\left(\dfrac{-4}{2}\right)^2\right)+42-6\left(\dfrac{-4}{2}\right)^2[/tex]

Simplify:

[tex]\implies f(x)=6\left(x^2-4x+\left(-2\right)^2\right)+42-6\left(-2\right)^2[/tex]

[tex]\implies f(x)=6\left(x^2-4x+4\right)+42-6\left(4)[/tex]

[tex]\implies f(x)=6\left(x^2-4x+4\right)+42-24[/tex]

[tex]\implies f(x)=6\left(x^2-4x+4\right)+18[/tex]

Factor the perfect square trinomial inside the parentheses:

[tex]\implies f(x)=6(x-2)^2+18[/tex]

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Comparing the derived equation with the vertex formula, the vertex of the derived equation is (2, 18).  Hence the completion of the square is correct.

The original price of purchasing is $825 plus 7% sales tax, then the interest will be $9.20. Hence, option D is correct.

The Latin term "per centum," which signifies "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship here between a component and a whole, in which the value of the whole is always assumed to be 100.

As per the given data in the question,

The original purchase price = $825

The sales tax = 7% of $825 = 825 × 7/100 = $57.75

Total credit = $825 + $57.75 = $882.75

The monthly interest rate = 12.5%/12 = 1.0417%

Interest = $882.75 × 1.0417/100

Interest = $9.20

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A. The lengths of the flower petals corresponding to the weeks 0, 1, 2, 3, 4, and 5 are 0, 3.09, 6.18, 9.27, 12.36, and 15.45, respectively.

B. The average rate of change of the function f(w) from week two to week five is 3.09.

C. The y-intercept of the function f(w) represents the initial length of the petal.

D. The reasonable domain to plot the growth function is week 0 to week 2.

The length of the flower petal and the weeks passed are denoted by f(w) and w. The equation of the function is given below.

f(w) = 3(1.03)w

The simplified function is f(w) = 3.09w.

The rate of change of the function from weeks 2 to 5 is calculated below.

R = [f(5) - f(2)]/(5 - 2)

R = [3.09*5 - 3.09*2]/3

R = 3.09*(5 - 2)/3

R = 3.09

The length of the flower petal at the end of the study was 3.48 cm. The length lies between the week 0 and the week 2.

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Answer: 6 ways

Step-by-step explanation:

The identification of the length of the missing section of each line, assuming that the lines are equally divided, is as follows:

a) The missing section is 24 units.

b) The missing section is 18 units.

c) The missing section is 10 units.

The missing sections can be computed using the mathematical operations of division and multiplication.

The product (quotient) of a division operation involves applying the divisor on the dividend using a division operand (÷).

The product of a multiplication operation applies the multiplier on the multiplicand using the multiplication operand (×).

a) The total units = 36

Division parts = 3

The units of each division = 12 (36/3)

The missing section = 24 (12 x 2)

b) The total units = 36

Division parts = 4

The units of each division = 9 (36/4)

The missing section = 18 (9 x 2)

c) The total units = 16

Division parts = 8

The units of each division = 2 (16/8)

The missing section = 10 (2 x 5)

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Answer: you should watch a quick video about it :)

Step-by-step explanation: