find the equation of the straight line with ng gradient and points. b) - 1/2, (2,3)​

[tex]y = 9x {}^{2} - 4 \\ flip \: x \: and \: y \\ x =9 (y ) {}^{2} - 4 \\ solve \: for \: the \: inverse \: of \: y \\ x + 4 = 9(y ) {}^{2} \\ y {} {}^{2} = \frac{x + 4}{9} \\ you \: can \: split \: it \: into \: two[/tex]

[tex]y {}^{(1)} = \sqrt{ \frac{x + 4}{9} } \\ y {}^{(2)} = - \sqrt{ \frac{x + 4}{9} } [/tex]

The weight of the puppy after the first month as described is; 26.65lbs.

Since, it follows from the task content that the initial weight of the puppy is; 20.5lbs and it gained 30% of this after 1 month, it follows that the weight of the puppy after one month is;

Weight = 20.5lbs × 130% = 26.65lbs.

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Answer: x=11

Step-by-step explanation:

The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.

4x-8 = 3x+3

x=11

Answer:

x = 11

Step-by-step explanation:

these angles are corresponding angles so they are equal to each other.

4x - 8 = 3x + 3 Subtract 2x from both sides

x - 8 = 3   Add 8 to both sides

x = 11

Plug 11 back into the equations find the angle measurements

4(11) -8 = 36 degrees

3(11) + 3 =  36degrees

Answer:

[tex]\textsf{1.} \quad C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

2.   [-273.15, ∞)

Step-by-step explanation:

Given:

[tex]C=\dfrac{5}{9}(F-32), \quad \text{where }F \geq -459.67[/tex]

To find the inverse of the given function, make F the subject:

[tex]\begin{aligned}C & =\dfrac{5}{9}(F-32)\\\implies \dfrac{9}{5}C & =F-32\\\implies F & = \dfrac{9}{5}C+32 \end{aligned}[/tex]

[tex]\textsf{Replace the } F \textsf{ with }C^{-1}(F)\textsf{ and the }C \textsf{ with } F:[/tex] :

[tex]\implies C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

The given domain of the function C(F) is F ≥ -459.67

Therefore, the minimum value of the function is:

[tex]\implies C(-459.67)=\dffrac{5}{9}(-459.67-32)=-273.15[/tex]

This means the range of the function C(F) is C(F) ≥ -273.15

The domain of the inverse function is the range of the function.

Therefore, the domain of the inverse function in interval notation is:  [-273.15, ∞)

Answer: -273.15

Step-by-step explanation:

Based on Cody Ray's credit card details and the unpaid-balance method, Cody Ray's unpaid balance is $144.44 and his previous balance is $144.44. His new balance is $147.04

His unpaid balance is:

= Purchases + Finance charge - (Payments + Credit)

= 376.90 + 17.54 - 250

= $144.44

Previous balance is the $17.54 finance charges.

New balance:

= Unpaid balance + Finance charge + New Purchases

= 144.44 + (144.44 x 1.8%)

= $147.04

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Answer:

  (d)  f(x) = -x²

Step-by-step explanation:

For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...

  f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)

  f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)

Of the offered answer choices, the only one with a vertex at the origin is ...

  f(x) = -x² . . . . . a=-1

Check the picture below.

The median value of x is 2.

According to the statement

we have given the values of x at some points then

and we have to find the median for the x.

We know that the median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.

and after put the values in this formula we get our median value for x.

So,

we have given that the f(x) is 0.2 when x is from -1 to 0

and f(x) is 0.2 +1.2x when x is grater than 0 but less than 1

and f(x) is 0 when x is less than -1 or grater than 1

From these statements it is clear that the the f(x) is only exist when the x lies in between from the -1 to 1.

So, the total value of x becomes is -1,0,1

Then according to the median formula

median = (n + 1) ÷ 2

median = (3+1) / 2

median = 2.

So, The median value of x is 2.

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Step-by-step explanation:

as the graphic shows, there are 2 objects : 1 block and 1 triangular shaped half-block.

the block is

7cm × 6cm × 2cm

the half-block is

8cm × 7cm × 6cm

with 10cm being the length of the tilted "roof" area.

the 2 sides facing each other are not visible to the observer, so, they are not part of the surface area of the composite figure.

let's start with the block :

top and bottom 7×2

front and back 6×2

no left (fully covered by the half-block)

right 6×7

that gives us :

2 × 7×2 = 2×14 = 28 cm²

2 × 6×2 = 2×12 = 24 cm²

6×7 = 42 cm²

in total : 94 cm²

the half-block :

top 10×7

bottom 8×7

front and back (triangles) 8×6/2

no left (due to being a half-block)

no right (fully covered by the block)

that gives us :

10×7 = 70 cm²

8×7 = 56 cm²

2 × 8×6/2 = 2×24 = 48 cm²

in total : 174 cm²

so, the complete surface area of the composite figure is

94 + 174 = 268 cm²

Answer:

C. [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

When you convert a fraction division into multiplication, you convert the divisor into its reciprocal. The reciprocal of [tex]\frac{2}{7}[/tex] is [tex]\frac{7}{2}[/tex]. So you get your answer  [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex].

The total amount of fencing they need = 38x + 10.

Perimeter for the rectangular fencing of the home = 160 yards

Perimeter for the square fencing of the pool = 40 yards

Perimeter of a rectangle = 2(length + width)

Perimeter of a square = 4(side length).

Perimeter for the rectangular fencing of the home = 2(3 + 10x + 2 + 5x) = 2(15x + 5) = 30x + 10

Perimeter for the square fencing of the pool = 4(2x) = 8x

The total amount of fencing they need = 30x + 10 + 8x = 38x + 10.

If x = 5, then:

Perimeter for the rectangular fencing of the home = 30x + 10 = 30(5) + 10 = 160 yards

Perimeter for the square fencing of the pool = 4(2x) = 8x = 8(5) = 40 yards.

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Answer:

38
160
40

Step-by-step explanation:

The domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}

The function is given as

g(x) = –⌊x⌋ + 3

The above is a step function, and the domain is the set of input values it can accept

Step functions of the given form can accept any real value of x

Hence, the domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}

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Complete question

The graph of the step function g(x) = –⌊x⌋ + 3 is shown. What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}

Answer:

A

Step-by-step explanation:

Answer:

Infinite solutions.

Step-by-step explanation:

 y = 5 - 2x

 2x + y = 5  ---------(I)

 a₁ = 2  ; b₁ = 1  and c = 5

4x + 2y = 10

a₂ = 4  ; b₂ = 2   and c₂  = 10

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac{1}{2}\\\\\dfrac{b_1}{b_2}=\dfrac{1}{2}\\\\\dfrac{c_1}{c_2}=\dfrac{5}{10}=\dfrac{1}{2}[/tex]

⇒  [tex]\sf \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}=\dfrac{1}{2}[/tex]

So, the line are coincident and has infinite solutions.

Answer:

sum

Step-by-step explanation:

example

2+3=5

The domain and the range of the function are given as follows:

b. Yes; domain: all re.al numbers; range: y greater-than-or-equal-to 0.

Since each input is related to only one output values, the graph is a function. It is defined for all values of x, assuming only non-negative values, hence the correct option is:

b. Yes; domain: all re.al numbers; range: y greater-than-or-equal-to 0.

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The points on the graph of (-4, 0), (-2.5, -12), and (0, -3), gives;

From the description of the graph, we have;

Furthest point left of the graph = (-4, 0)

The furthest point right on the graph = (0, -3) = The maximum point

The minimum point = (-2.5, -12)

F(x) < 0 at the minimum point

The minimum point is to the right of x = -4

The point the graph crosses the y-axis = (0, -3)

Therefore;

The interval of the graph where F(x) is larger than 0 is to the left of (-4, 0), is the interval (-∞, -4)

The true statement is therefore;

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The Surface area of the triangular prism with the net shown below is 106 cm²

An equation is an expression that shows the relationship between two or more variables and numbers.

Surface area of the triangular prism = 2(0.5 * 5 * 3) + (7 * 3) + 2(7 * 5) = 106 cm²

The Surface area of the triangular prism with the net shown below is 106 cm²

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[tex] \underline{ \orange{\huge \boxed{ \frak{Answer : }}}}[/tex]

Let ,

[tex] \sf \large \color{purple} y = 2 {x}^{3} - 3 {x}^{2} - 12x + 10 \: --( \: 1 \: )[/tex]

[tex] \: \: \: [/tex]

Now , Diff wrt ' x ' , we get :

[tex] \sf \: \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} - 3 {x}^{2} - 12x + 10) \\ \sf \: \sf \: \frac{dy}{dx} = \frac{d}{dx} \: 2(3 {x}^{2} ) - \frac{d}{dx} 3 {x}^{2} - \frac{d}{dx} 12x + \frac{d}{dx} 10 \\ \sf \: \frac{dy}{dx} =2(3 {x}^{2} ) - 3(2x) - 12(1) + 0 \\ \sf \: \frac{dy}{dx} =6 {x}^{2} - 6x - 12 + 0 \\ \: \sf \red{\frac{dy}{dx} = 6 {x}^{2} 6x - 12 -- (2)}[/tex]

[tex] \: \: \: [/tex]

For maxima or minima \frac{dy}{dx} = 0

[tex] \: \: \: [/tex]

[tex] \sf \: 6 {x}^{2} - 6x - 12 = 0[/tex]

[tex] \: \: \: [/tex]

Divided by 6 on both side , we get.

[tex] \: \: \: [/tex]

[tex] \sf \: {x}^{2} - x - 2 = 0 \\ \sf \: {x}^{2} - 2x + x - 2 = 0 \\ \sf \: x(x - 2) + 1(x - 2) = 0 \\ \sf \: (x - 2)(x + 1) = 0 \\ \sf \: x - 2 = 0 \: \: \bold or \: \: x + 1 = 0 \\ \sf \fbox{x = 2 \: } \: \bold or \: \fbox{ x = - 1}[/tex]

[tex] \: \: \: [/tex]

Again Diff wrt ‘ x ’ , we get.

[tex] \sf \: \frac{d}{dx} =(\frac{dy}{dx} ) = 6\frac{d}{dx} - 6\frac{d}{dx}x - \frac{d}{dx}12 \\ \sf \: \frac{ {d}^{2}y }{ {dx}^{2} } = 6(2x) - 6(1) - 0 \\ \sf \: \sf \bold{ \frac{ {d}^{2}y }{ {dx}^{2} } =12x - 6}[/tex]

[tex] \: \: \: [/tex]

At x = 2

[tex] \: \: \: [/tex]

[tex]\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12(2) - 6 \\ \: \: \: \sf \: = 24 - 6 \\ \: \: \: \: \sf \red{ = 18 > 0}[/tex]

At x = -1

[tex] \: \: \: [/tex]

[tex]\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12( - 1) - 6 \\ \: \: \: \sf \: = - 12 - 6 \\ \: \: \: \: \sf \red{ = - 18 < 0 }[/tex]

[tex] \: \: \: [/tex]

x = 2 gives minima value of function.

[tex] \: \: \: [/tex]

x = -1 gives maxima value of function.

[tex] \: \: \: [/tex]

Now, put x = 2 in eqⁿ ( 1 )

[tex] \: \: \: [/tex]

[tex] \sf \: y \: minima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( {2})^{3} - 3 ({2})^{2} - 12(2) + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: = 2(8) - 3(4) - 24 + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: = 16 - 12 - 24 + 10 \\\sf \: \: \: \: \: \: \: \: \: \: = - 20 + 10 \\\sf \color{red}{\boxed{ = - 10}}[/tex]

[tex] \: \: \: [/tex]

The Point of minima is ( 2 , -10 ).

[tex] \: \: \: [/tex]

Now , put x = -1 in eqⁿ ( 1 )

[tex]\sf \: y \: maxima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( { - 1})^{3} - 3 ({ - 1})^{2} - 12( - 1) + 10 \\\sf \color{red}{\boxed{ = 17}}[/tex]

[tex] \: \: \: [/tex]

The point of maxima value is ( -1 , 17 ).

[tex] \: \: \: [/tex]

[tex] \: \: [/tex]

Hope Helps! :)

The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.

It follows from the task content that the equation which could be used to find the length of the third side be determined.

Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.

Hence, the required equation is; 5 squared + 8 squared = c squared.

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Answer:

The answer is A
5 squared + 8 squared = c squared

Step-by-step explanation:

Answer:

-0.4 or [tex]\frac{-2}{ 5}[/tex]

Step-by-step explanation:

[tex]tan^-^{1} ({\frac{2}{5} })=21.80\\[/tex]

tan ( 2π-21.80)

but 2π = 360

Therefore our question becomes:

tan ( 360-21.80)=tan(338.2)= -0.4

Answer:

Step-by-step explanation:

a = number of successful events

b = total number of events.

Answer:

the answer is 22

Step-by-step explanation:

12,15,22,37,49

since 22 is in the middle its the median (make sure you put the #'s from least to greatest)

Answer:

22

Step-by-step explanation:

22, 37, 49, 15, 12

First put the data set from least to greatest.

12, 15, 22, 37, 49

The median is the middle number of the data. In this case, the median is 22.

Hope this helps!

Using the probability concept, the correct statement is:

B. P(hibiscus|red) = P(hibiscus).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, the probabilities are:

Same probabilities, hence the statement that they are different is false.

For item b, the probabilities are:

Equal, hence this is the correct statement.

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Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:

p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.

Hence, out of 44,000 adults, the expected number is found as follows:

0.4412 x 44000 = 19,413.

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Using an exponential function, it is found that:

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

The parameters for this problem are given as follows:

a = 2, b = 2.

Hence the number of bacteria after x hours is given by:

[tex]y = 2(2)^x[/tex]

After 6 hours, the amount is:

[tex]y = 2(2)^6 = 2^7 = 128[/tex]

After 24 hours, the amount is:

[tex]y = 2(2)^{24} = 2^{25} = 33554432[/tex]

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A simple main effect analysis looks at the mean difference at each level of the independent variable.

Given With a simple main effect, the analysis examines.

Simple effects are also called the main effects of design of experiments. The main effect can be defined as the effect of the explanatory variables measured on a particular criterion or response variable of the study. It's easy to say that what happens within the level of the explanatory variables is the difference. In a factorial experiment, the simple main effect is that one independent variable is at a specified level of another. The main effect of one independent variable is averaged across the levels of the other independent variable. For a simple main effect, the results are analyzed as if a separate experiment was performed at each level of the other independent variables.

Therefore, a simple main effect analysis looks at the mean difference at each level of the independent variable.

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The total cost in 5 hours is $225

Given that the charges of a supply fee of an artist is $50

The charges per hour classes is $35

The total cost is expressed by c

The number of hours expressed by h

We need to calculate the total cost in 5 hour lesson

As per the given statement ,

C= 50 +35h

Where h is the number of hours

h = 5 hours

C = 50 + 35h

C = 50 + 35(5)

C = 50 +175

C = $225

The total cost in 5 hours is $225

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Answer:

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.