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» Rewrite the expression 110.3-5 using only positive exponents.
First rewrite 11º.
11⁰.3-5
=

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

Step-by-step explanation:

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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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:

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:

6

Step-by-step explanation:

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

cardinal number = 6

Answer: 210 liters

Step-by-step explanation:

Answer:

nik

Step-by-step explanation:

Answer:

  (-2, -5), (2, 11)

Step-by-step explanation:

You want the coordinates of the points on the curve y = x³ +3 where the tangent lines are parallel to y = 12x -1.

The slope of the tangent line is the x-coefficient in its equation: 12.

The slope of the curve is given by its derivative:

  y' = 3x²

We want the x-values where the slope is 12. These are the solutions to ...

  12 = 3x²

  4 = x² . . . . . . . . . . divide by 3

  x = ±√4 = ±2 . . . . . take the square root

The coordinates of the points with x = ±2 are ...

  y = (±2)³ +3 = ±8 +3 = {-5, 11}

The tangent points are (-2, -5) and (5, 11).

__

Additional comment

The attached graphs and table show the solutions to y'=0 and the corresponding point locations. It also shows the tangent line equations (in point-slope form).

Answer: 6 ways

Step-by-step explanation:

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

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:

wean positive realtionship

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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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: y=-2x²-6x

Step-by-step explanation:

Its x-intercepts are 0 and -3, and the graph goes through the point (-1,4)

Hence we have three coordinates of the equation y=ax²+bx+c    (1):

                                    (0,0)   (-3,0)   (-1,4)

Let's substitute these coordinates into formula (1):

[tex]0=a(0)^2+b(0)+c\\0=a(-3)^2+b(-3)+c\\4=a(-1)^2+b(-1)+c\\\\0=0+0+c\\0=9a-3b+c\\4=a-b+c\\\\0=c\\0=9a-3b+0\\0=a-b+0\\\\c=0\\9a-3b=0\ \ (1)\\a-b=4\ \ \ \ \ (2)\\\\c=0\\\\[/tex]

Divide both parts of the equation (1) by 3 and multiply both parts of the equation (2) by -1: :

[tex]3a-b=0\\-a+b=-4\\\\[/tex]

Sum these equations:

[tex]2a=-4[/tex]

Divide both parts of the equation by 2:

[tex]a=-2[/tex]

We substitute the value of a=-2 into equation (2):

[tex]-2-b=4\\[/tex]

Divide both parts of the equation by -1:

[tex]2+b=-4\\\\2+b-2=-4-2\\\\b=-6[/tex]

[tex]Thus, \\\\y=-2x^2-6x+0\\\\y=-2x^2-6x[/tex]

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:

[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 diagram that matches the given situation is as shown below.

The correct answer is an Option C

We know that, in the mapping of functions, we map certain parameters to a set of other parameter functions.

In this question, we have been given the function h relates Kami's age in years to her height in inches on her birthday that year.

It means that her ages would be one-one the left to map her height. that means there were 2 times were despite her age difference, her height remained the same.

From the given options, the correct one that represents the required mapping is:

h(14) = 64

h(15) = 64

Therefore, the diagram that matches the given situation is as shown below.

The correct answer is an Option C

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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. 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:

[tex]m=6[/tex]

Step-by-step explanation:

Start by subtracting 3 from both sides

[tex]15=2m+3\\15-3=2m+3-3\\12=2m[/tex]

Now, divide both sides by 2!

[tex]\frac{12}{2}=\frac{2}{2}m\\ 6=m\\ m=6[/tex]

Answer:

m=6

i think this help you

The y-coordinate of the y-intercept of the polynomial function is -36.

Given:

polynomial function defined below.

f(x) = (x + 6) (5x² + 2)(x − 3)

To find y intercept put x = 0 in the function.

y = (0+6)(5*0^2+2)(0-3)

= 6*(5*0+2)*(-3)

= 6*(0+2)(-3)

= 6*2*(-3)

= 12(-3)

= -36

Therefore The y-coordinate of the y-intercept of the polynomial function is -36.

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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:

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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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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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 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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Answer:

Boss's statement is not misleading.

Explanation:

To find the median, we need to find the middle number.

8.00, 8.50, 9.00, 9.50, 10.00, 23.50

9.00 and 9.50 are in the middle.

And in the middle of those two is 9.25.