Identify the equivalent expressions of 4(2x + x-3) - 3x + 3 by substituting x = 2 and x = 3.
9x - 9
9x - 1
9x + X-9
9(x - 1)
4(3x - 3) + 3 - 3x

a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.

Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²

The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²

b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.

Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,

Area of Striped Region : 40 - 22 = 18 m²

Answer:

[tex]x = -\frac{3}{2}[/tex] or [tex]x = 1[/tex]

Step-by-step explanation:

Using the zero product property, first step is to set the given equation, [tex] 2x^2 + x - 1 = 2 [/tex] , to zero. Then factorise the left side.

Thus,

[tex] 2x^2 + x - 1 = 2 [/tex]

Subtract 2 from both sides

[tex] 2x^2 + x - 1 - 2 = 2 - 2 [/tex]

[tex] 2x^2 + x - 3 = 0 [/tex]

Factorise the left side

[tex] 2x^2 + 3x - 2x - 3 = 0 [/tex]

[tex] x(2x + 3) - 1(2x + 3) = 0 [/tex]

[tex] (x - 1)(2x + 3) = 0 [/tex]

Find the solution

[tex] x - 1 = 0 [/tex]

Or

[tex]2x + 3 = 0[/tex]

[tex] x = 1 [/tex]

Or

[tex]2x + 3 = 0[/tex]

[tex]2x = -3[/tex]

[tex]x = -\frac{3}{2}[/tex]

The answer is: [tex] x = 1 [/tex] or [tex]x = -\frac{3}{2}[/tex]

Answer:

A. 70.69 is the correct answer.

Step-by-step explanation:

Given:

Two lines:

[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]

To find:

Angle between the two lines = ?

Solution:

Acute Angle between two lines can be found by using the below formula:

[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]

Where [tex]\theta[/tex] is the acute angle between two lines.

[tex]m_1, m_2[/tex] are the slopes of two lines.

Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:

[tex]m = -\dfrac{a}{b }[/tex]

So,

[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]

[tex]m_2 = -\dfrac{2}{ 3}[/tex]

Putting the values in the formula:

[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]

So, correct answer is A. 70.69

Answer:

2.5 meters

Step-by-step explanation:

Answer:

since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its off functions

Step-by-step explanation:

set = {0,1,2,3,4,5,6,7,8,9}

setting up a one-to-one correspondence between the set of real numbers between 0 and 1

The function : F(n)= {0,1} is equivalent to the subset (sf) of (n) , this condition is met if n belongs to the subset (sf) when f(n) = 1

hence The power set of (n) is uncountable and is equivalent to the set of real numbers given

since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its offfunctions

Answer:

Question is incomplete but use below

Step-by-step explanation:

you can do total = (price of cheese pizza) ( amount of cheese pizzas bought)+(price of pepperoni pizza) ( amount of pepperoni pizzas bought)

Answer: 3

Step-by-step explanation:

first, we know that:

1 + 2 + 3 + 4 +5 +6 = 21

Now, which two numbers we should take out in order to have 15?

we can remove the 2 and the 4, or the 1 and the 5.

so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)

in the other arrange, we have that removing two numbers we should get 12.

in order to reach 12, we should remove two numbers that add 9 together.

those can be 4 and 5, or 6 and 3.

Now, notice that in the first restriction we have that:

Or 2 and 4 are opposite,

or 1 and 5 are opposite.

So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.

Then we can affirm that the value that appears in the face opposite to the 6, is the 3.

Answer:

I'm confused by this. What do they mean by prove?

Step-by-step explanation:

Answer:

9 m

Step-by-step explanation:

Given that

Width of rectangular flower garden, w = 4 m

Perimeter of rectangular flower garden, p = 26 m

To find:

Length of Lisa's flower garden = ?

Solution:

First of all, let us understand perimeter, length and width of a rectangle.

Let ABCD be a rectangle. Please refer to the attached image.

Opposite sides of a rectangle are equal to each other.

AB = CD = Length  

Let the length be [tex]l[/tex] m.

BC = DA = Width = 4 m

Perimeter of a closed image is equal to the sum of all the sides of the image.

So, perimeter of ABCD:

[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]

[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]

Answer:

[tex]\sqrt{51}[/tex] units.

Step-by-step explanation:

Point E is inside a rectangle ABCD.

Please refer to the attached image for the given statement and dimensions.

Given that:

Sides AE = 6 units

BE = 7 units and

CE = 8 units

To find:

DE = ?

Solution:

For a point E inside the rectangle the following property hold true:

[tex]AE^2+CE^2=BE^2+DE^2[/tex]

Putting the given values to find the value of DE:

[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]

Answer:

3 only

Step-by-step explanation:

Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.

Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.

Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.

Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.

Therefore, the true statement is III only.

More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.

Data given in the table shows the data of elections between two candidates among the different cities.

Statistics is the study of mathematics that deals with relations between comprehensive data.

I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.

II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false

III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.

IV. Overall, more residents support candidate A than candidate B. it is also false.

Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.

Learn more about Statistics here:
https://brainly.com/question/23091366

#SPJ5

Answer:

Answer:

  x < -1

Step-by-step explanation:

Since the parabola opens upward, it is positive and decreasing where the left branch is above the x-axis: all points to the left of x=-1.

  all real values of x where x < -1

Answer:

  0 ≤ x ≤ 10

Step-by-step explanation:

The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...

  -x^2 +10x ≥ 0

  x(10 -x) ≥ 0

The two factors in this product will both be positive only for values ...

  0 ≤ x ≤ 10 . . . . the domain of f(x)

This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.

Answer:

(9, -13.5)

Step-by-step explanation:

It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.

Rule for dilation is,

(x, y) → (kx, ky)

where 'k' is the scale factor.

If vertex R of the quadrilateral is (6, -9),

By the given rule of dilation,

R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]

           → R'(9, -13.5)

Therefore, Option given in bottom right (9, -13.5) will be the answer.

Answer:

The probability is  [tex]p(n ) = 3.18*10^{-5}[/tex]

Step-by-step explanation:

From the question we are told that

     The population size is  N =  31

      The sample size  n =  4  

Generally the number of way by which the n  can be selected from N is mathematically represented as

          [tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]

The number of ways of selecting a particular sample size is  is   [tex]k = 1[/tex]

Therefore the probability of each simple random sample in this​ case is mathematically evaluated as  

           [tex]p(n ) = \frac{1}{31465}[/tex]  

           [tex]p(n ) = 3.18*10^{-5}[/tex]

Answer:

40

Step-by-step explanation:

In the question only lies the answer:

"and a total of forty students plan to participate in cross country."

Answer:

2

Step-by-step explanation:

2

Answer:

70%

Step-by-step explanation:

The method to find out percentage increase is by subtracting the original price from the increased price and making it into a fractional form with the denominator as 10 (out of 100%). So it results to this.

(original price - increased price) / 10

(17 - 10) / 10 = 7/10

7/10 can be converted from its fractional form to 70% i.e.its percentage.

Hope this helps and please mark as the brainliest.

A(t) = 100t^2 + 500t + 625

3,025 square pixels

Answer:

A(t) equals 100t²+ 500t + 625.

The area of the square image after 3 seconds is 3,025 square pixels.

Answer:

[tex]\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

When the parabola equation is like

[tex]y=a(x-h)^2+k[/tex]

The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))

As the vertex is (3,-2) we can say that h = 3 and k = -2.

We need to find a.

The focus  is (3,2) so we can say.

[tex]2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}[/tex]

So an equation for the parabola is.

[tex]\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

C

Step-by-step explanation:

The first sentence basically sets up the equation which is given, so we can read it for knowledge but it is not crucial to solve the problem.

We start here:

we are given: $120 - 0.2($120)

= 120 - (0.2)(120)   (factoring out 120)

= 120 (1 - 0.2)

= 120 (0.8)

= 0.8 (120)     (answer c)

Answer:

1

Step-by-step explanation: diliation is like multiplilcation if you were to do 3*1 =3. simply congruent means all sides and angles are the same.  

Given that the image and the preimage of the triangle are congruent, their

dimensions are the same.

Reasons:

Let ΔABC represent the preimage, and let ΔA'B'C' represent the image.

Given that the image and the preimage are congruent, we have;

AB ≅ A'B'

BC ≅ B'C'

AC ≅ A'C'

By definition of congruency, we have;

AB = A'B'

BC = B'C'

AC = A'C'

The scale factor of dilation is given as follows;

Therefore;

Learn more about dilation transformation here:

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Answer:

[tex]\large \boxed{{y=18}}[/tex]

Step-by-step explanation:

[tex]1(y+3)=2(y+-4)+- 7[/tex]

Expand brackets.

[tex]y+3=2y-8+- 7[/tex]

Simplify.

[tex]y+3=2y-15[/tex]

Add -y and 15 on both sides.

[tex]y+3-y+15=2y-15-y+15[/tex]

Simplify.

[tex]3+15=2y-y[/tex]

[tex]18=y[/tex]

Answer:

18

Step-by-step explanation:

● 1 (y+3) = 2 (y+(-4) )+ (-7)

When you multiply by 1 you get the same result.

● y+3 = 2 (y+(-4))+(-7)

When you have a + sign with a - sign write -.

● y+3 = 2(y-4)-7

Multiply 2 by (y-4) and simplify

● y+3 = (2y-8)-7

● y+3 = 2y -8-7

● y+3 = 2y -15

Add 15 to both sides

● y +3+15 = 2y-15 +15

● y + 18 = 2y

Sibstract y from both sides

● y +18 - y = 2y -y

● 18 = y

Answer:

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

After 11 hours of burning, a candle has a height of 23.4 centimeters.

After 30 hours of burning, its height is 12 centimeters.

What is the height of the candle after 13 hours?

:

Assign the given values as follows:

x1 = 11; y1 = 23.4

x2 = 30; y2 = 12

:

Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29

m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19

:

Find the equation using the point/slope formula: y - y1 = m(x - x1)

y - 23.4 = -11.4%2F19(x - 11)

y - 23.4 = -11.4%2F19x + 125.4%2F19

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19

y = -11.4%2F19x + 570%2F19

y = -11.4%2F19x + 30, is the equation

:

What is the height of the candle after 13 hours?

x = 13

y = -11.4%2F19(13) + 30

y = -148.2%2F19 + 30

y = -7.8 + 30

y = 22.2 cm after 13 hrs

Answer:

the answer is 18

Step-by-step explanation:

8 is the answer

0riginal break even point:

285000/ 60/35 = $166,250

New break even point = new fixed costs / ( selling price - variable cost/ selling price)

New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60

300,900 / 60-30.50/60 = $612,000

The new break even point increases.

Answer:

(a) 1.341

(b) -2.539

(c) -2.160 and 2.160

Step-by-step explanation:

(a) We have to find the critical​ value(s) for a​ right-tailed test of a population mean at the alpha = 0.10 level of significance with 15 degrees of freedom. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 15 and the level of significance for a right-tailed test is 0.10, i.e. P = 10%

Now, looking in the t table with P = 10% and [tex]\nu[/tex] = 15, we get the critical value of 1.341.

(b) We have to find the critical​ value(s) for a​ left-tailed test of a population mean at the alpha = 0.01 based on a sample size of n = 20. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 20 - 1 = 19 and the level of significance for a left-tailed test is 0.01, i.e. P = 1%

Now, looking in the t table with P = 1% and [tex]\nu[/tex] = 19, we get the critical value of 2.539. But since it is a left-tailed test, so the critical value will be -2.539.

(c) We have to find the critical​ value(s) for a​ two-tailed test of a population mean at the alpha = 0.05 level of significance based on a sample size of n = 14. ​

Since the degrees of freedom are included here, so we will use t table here for a population mean test.

In the table there are two values given, one is the degrees of freedom and another is the value of P.

P is the level of significance at which the critical values are calculated.

So, here the degrees of freedom (n - 1) = 14 - 1 = 13 and the level of significance for a two-tailed test is [tex]\frac{0.05}{2}[/tex] is 0.025, i.e. P = 2.5%.

Now, looking in the t table with P = 2.5% and [tex]\nu[/tex] = 13, we get the critical value of -2.160 and 2.160 for a two-tailed test.

let the numbers be a and b, a>b

a+b=6(a-b)

we need to find reciprocal of ratio of larger to smaller , which will be same as ratio of smaller to larger or b/a, let's call it x

divide the equation by a.

1+x=6(1-x)

on solving, x=5/7