A mystery number is greater than 50 and less than 100. You can make exactly five different rectangles with the mystery number of tiles. (Hint: This means the mystery number is a square number). Its prime factorization consists of only one prime number. What is the mystery number?

Answer:

[tex]\dfrac{3}{2}[/tex]

Step-by-step explanation:

If 2x - 3 is a factor of P(x), then  3/2 is a zero of P(x).

[tex]\begin{array}{rcl}2x - 3 & = & 0\\2x & = & 3\\\\x & = & \mathbf{\dfrac{3}{2}}\end{array}\\\\\mathbf{P(\frac{3}{2})} \text{ will equal zero if $(2x-3)$ is a factor of $P(x)$}[/tex]

Answer:

A. Drusilla

Step-by-step explanation:

The line of random numbers is used for numbered population.

As we can see that the students are already labelled we have to divide the random number line in pairs of 2 digits

59,78,44,43,12,15,95,40,92,33,00,04,67,43,18,02,61,05,73,96,16,84,33,84,54

We have to keep in mind that our serial numbers are till 29.

So read the pair of numbers one by one

59 can't be used as it is greater than 29. Similarly 78,44,43 cannot be used.

The first student will be: 12 Kiefer

Then 15 and 00 will be second and third.

So the fourth student will be: 04 Drusilla

Hence option A is correct ..

Answer:

answer C:  (x - 1) is also a factor of P(x).

Step-by-step explanation:

Synthetic division is the best approach here.  Given that one factor is x - 9, we know that 9 is the appropriate divisor in synthetic division:

9    )    5    -51      k       -9

                 45    -54      (9k - 486)

      ----------------------------------

           5     -6   (k - 54)  (-9 + 9k - 486)

and this remainder must = 0.  Find k:  -9 + 9k - 486 = 0, or

                                                                      9k = 486 + 9 = 495

                                                                      Then k = 495/9 = 55

Look at the last line of synthetic division, above:

5   -6   (k - 54)    0

Substituting 55 for k, we get:

5   -6     1          

These are the coefficients of the quotient obtained by

dividing P(x) by (x - 9).    They correspond to 5x^2 - 6x + 1.

We must factor this result.

Let's start with 5x + 1, and check whether this is a factor of 5x^2 - 6x + 1 or not.  If 5x + 1 is a factor, then the related root is -1/5.  Let's use -1/5 as the divisor in synthetic div.:

-1/5    )       5       -6        1

                           -1        7/5

         ----------------------------

                 5        -7       12/5       Here the remainder is not zero, so -1/5 is

                                                    not a root and 5x + 1 is not a factor.

Now try x - 5.  Is this a factor of 5x^2 - 6x + 1?  Use 5 as divisor in synth. div.:

5    )     5      -6      1

                    25    95

     ------------------------

         5         19     96  Same conclusion:  x - 5 is not a factor.

Try x = -1:

-1     )    5     -6     1

                    -5     11

        ----------------------

            5       -11     12.  The remainder is not zero, so (x + 1) is not a factor.

Finally, try x = 1:

1     )    5    -6     1

                  5    -1

      --------------------

          5     -1      0

Finally, we get a zero remainder, and thus we know that x - 1 is a factor of P(x)

Answer C is correct:  x - 1 is a factor of P(x)

To solve this question, we can apply the Remainder Theorem. According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( x - c \), the remainder of the division is \( P(c) \).
Given:
\( P(x) = 5x^3 − 51x^2 + kx − 9 \)
We are told that when \( P(x) \) is divided by \( x − 9 \), the remainder is 0. Therefore, according to the Remainder Theorem:
\( P(9) = 5(9)^3 − 51(9)^2 + k(9) − 9 = 0 \)
Let's compute \( P(9) \):
\( P(9) = 5(729) − 51(81) + 9k − 9 \)
\( P(9) = 3645 − 4131 + 9k − 9 \)
\( P(9) = 9k − 495 = 0 \)
To solve for \( k \):
\( 9k = 495 \)
\( k = 495 / 9 \)
\( k = 55 \)
Now, we know that P(x) with \( k = 55 \) has no remainder when divided by \( x − 9 \).
The updated polynomial \( P(x) \) is:
\( P(x) = 5x^3 − 51x^2 + 55x − 9 \)
To determine which of the given options is a factor of \( P(x) \), we will test each option by plugging in the roots of these factors into the polynomial \( P(x) \) and checking if it yields zero.
A) For \( x − 5 \), the root is \( x = 5 \):
\( P(5) = 5(5)^3 − 51(5)^2 + 55(5) − 9 \)
\( P(5) = 5(125) − 51(25) + 275 − 9 \)
\( P(5) = 625 − 1275 + 275 − 9 \)
\( P(5) = 625 − 1009 \)
\( P(5) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
B) For \( x + 1 \), the root is \( x = -1 \):
\( P(-1) = 5(-1)^3 − 51(-1)^2 + 55(-1) − 9 \)
\( P(-1) = -5 − 51 − 55 − 9 \)
\( P(-1) = -120 \)
\( P(-1) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
C) For \( x − 1 \), the root is \( x = 1 \):
\( P(1) = 5(1)^3 − 51(1)^2 + 55(1) − 9 \)
\( P(1) = 5 − 51 + 55 − 9 \)
\( P(1) = 60 − 60 \)
\( P(1) = 0 \) (This factor yields zero, so it is a factor of \( P(x) \).)
D) For \( 5x + 1 \), the root is \( x = -1/5 \):
\( P(-1/5) = 5(-1/5)^3 − 51(-1/5)^2 + 55(-1/5) − 9 \)
\( P(-1/5) = -1/25 − 51/25 − 55/5 − 9 \)
Since the coefficients add up to a non-zero value, we can tell that it's not going to be zero; therefore, it is not worth computing the whole expression.
\( P(-1/5) ≠ 0 \) (Hence, this is also not a factor of \( P(x) \).)
The only option that gives a remainder of zero when its root is substituted into \( P(x) \) is C, \( x - 1 \). Therefore, the correct answer is:
C- x − 1

Answer:

55

Step-by-step explanation:

bisect means to cut in half so it is half of 110 so it is 55

Answer:

I believe the answer is 55°.

Step-by-step explanation:

Sense line Y is cut between angle AXB, you would need to find the half of 110°.

So, 110 ÷ 2 = 55.

Therefore, 55° is the correct answer.

Question 2

Answer: 1.20

---------

To get this answer, you divide the total amount of royalties (300) over the number of books (250) to get 300/250 = 1.20

Another way to see this is through the ratio of

300 dollars: 250 books

then you divide both parts of that ratio by 250 so that the "250 books" turns into "1 book" like so...

300 dollars: 250 books

300/250 dollars: 250/250 books

1.20 dollars: 1 book

Indicating that his royalties per book is 1.20 dollars. The rate of change is often expressed as a unit rate, meaning that we want the royalties for 1 book (which then scales up).

=========================================================

Question 3

Answer: slope is -1/10 or -0.1; slope tells us how much the candle height is decreasing each minute, y intercept is the starting candle height (see below for further explanation)

---------------

Explanation:

The y intercept is at 25, as this is where the diagonal line crosses the vertical y axis. Similarly, the x intercept is 250. The y and x intercept lead to the two points (0,25) and (250,0). Let's use the slope formula to find the slope of the line through these two points

m = (y2 - y1)/(x2 - x1)

m = (0 - 25)/(250 - 0)

m = -25/250

m = -1/10

m = -0.1

The slope of the line is -1/10 or the decimal equivalent -0.1

What does the slope tell us? It tells us how much of the candle's height is changing as each minute ticks by. Specifically, the slope -0.1 means that the candle height is going down by 0.1 cm for each minute gone by. A shorter way to say this is to say "the height is decreasing by 0.1 cm per minute" (think of it like a speed such as miles per hour)

The y intercept is the starting height of the candle due to the fact that x = 0 here. Therefore, the starting height of the candle is 25 cm.

Side note: the x intercept of 250 tells us how long the candle burns for, which in this case is 250 minutes (4 hrs, 10 min) because y = 0 for the x intercept, and y is the height of the candle at time x. Anything beyond x = 250 is not possible in realistic sense as we can't have a negative y height value.

Answer:

f(x) reflects across the x-axis and translate left 2 ⇒ 2nd answer

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ f(x) = x²

∵ The parent function is f(x) = - (x + 2)²

- There is a negative out the bracket means we change f(x) to -f(x)

∴ f(x) is reflected across the x-axis

- The x is changed to x + 2, that means we translate the f(x) to the

  left two units

∵ x in f(x) is changed to (x + 2)

∴ f(x) is translated 2 units to the left

∴ f(x) reflects across the x-axis and translate left 2

The function f(x) = -(x + 2) ^2 is a reflection over the x-axis and a horizontal shift to the left by 2 units.

The given function, f(x) = -(x + 2) ^2, is a transformation of the parent function, f(x) = x^2. The negative sign in front of the function reflects it over the x-axis, making it an upside-down parabola. The addition of 2 inside the parentheses shifts the graph 2 units to the left. Therefore, the transformation is a reflection over the x-axis and a horizontal shift to the left by 2 units.

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Answer:

associative property

Step-by-step explanation:

This illustrates the associative property.  It doesn't matter in which order you combine the terms here.

This is an example of associative property which states,

[tex]a+(b+c)=(a+b)+c[/tex]

Hope this helps.

r3t40

Answer:

y + 3 = -6(x + 9) or y = -6x - 57

Step-by-step explanation:

We can use the point-slope form for this situation.

Point-slope form: y - y₁ = m(x - x₁), where m = slope and (x₁, y₁) are given coordinates.

Plug in: y + 3 = -6(x + 9)

This can be changed to the more common slope-intercept form.

Multiply: y + 3 = -6x - 54

Subtract: y = -6x -57

Answer:

y=-6x-57 (this answer is in slope-intercept form)

I don't know what your choices are and if you can select multiple answers or not.

Step-by-step explanation:

y=mx+b is an equation for a line with slope m and y-intercept b.

We are given m=-6 so we will plug this in giving us: y=-6x+b.

Now we need to find b, the y-intercept.  Let's use a point (x,y) we know is on the line of y=-6x+b to find b.

We know (x,y)=(-9,-3) is on that line.  So our line should satisfy this point.  We must pick a b so that happens.  Plug (x,y)=(-9,-3) into the equation now.

-3=-6(-9)+b

-3=54+b

-3-54=b

-57=b

So the equation is y=-6x-57

Answer:

x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6 thus NO, x^2 - (7 x)/3 = -4  would be correct.

Step-by-step explanation:

Solve for x:

3 x^2 - 7 x + 12 = 0

Hint: | Write the quadratic equation in standard form.

Divide both sides by 3:

x^2 - (7 x)/3 + 4 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 4 from both sides:

x^2 - (7 x)/3 = -4

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 49/36 to both sides:

x^2 - (7 x)/3 + 49/36 = -95/36

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 7/6)^2 = -95/36

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 7/6 = (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6

Hint: | Look at the first equation: Solve for x.

Add 7/6 to both sides:

x = 7/6 + (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6

Hint: | Look at the second equation: Solve for x.

Add 7/6 to both sides:

Answer:  x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6

Answer:

Joseph's work wasn't accurate

Step-by-step explanation:

Take a look at the image to understand the procedures

x^3 + 7x^2 -8x -3x^2 -21x +24

x^3 + 4x^2 -29x +24

For this case we must simplify the following expression:

[tex](x-3) (x ^ 2 + 7x-8)[/tex]

We must apply distributive property:

[tex]x * x ^ 2 + x * 7x-8 * x-3 * x ^ 2-3 * 7x + 3 * 8 =\\x ^ 3 + 7x ^ 2-8x-3x ^ 2-21x + 24 =[/tex]

Adding similar terms we have:

[tex]x ^ 3 + 4x ^ 2-29x + 24[/tex]

Answer:

The simplified expression is:

[tex]x ^ 3 + 4x ^ 2-29x + 24[/tex]

Answer:

It is not a function!

Step-by-step explanation:

It is not a function!

A function can't have two y-values assigned to the same x-value. In this case, you can se that for x=1 we have two y-values, which are y= -2 and y= -3.

We can have have two x-values assigned to the same y-value, that's why it's okay that for x=1 and x=3 we have the same y-value y=-2

Answer:

B -0.104

Step-by-step explanation:

Step 1: Write the formula for correlation

r =    total xy

√Total x² x Total y²

Step 2: Make a table to calculate all values

Table is attached in the picture below

Step 3 : Solve

Mean of X = Total X/ Total number of X

                  = 507/12

                  = 106.33

Mean of Y = Total Y/ Total number of Y

                  = 1276/ 12  

                  = 42.25

r =    total xy

√Total x² x Total y²

r = -352.05/ √3656.25 x 3122.66698

r = -0.104

-0.104 is negative

This negative correlation means there is an inverse correlation between variables.

Answer:

B. According to this data, there is a negative correlation between age and IQ.

Step-by-step explanation:

Correlation shows the strength of relation between two variables. The formula used to calculate correlation is:

[tex]Correlation(r) = \frac{Cov(x, y)}{\sigma_{x}\sigma_{y}}= \frac{E(x-\mu_{x})(y-\mu_{y})}{\sigma_{x}\sigma_{y}}[/tex]

where, Cov(x,y) = Covariance of x and y

[tex]\sigma_{x} [/tex] = standard deviation of x

[tex]\sigma_{y} [/tex] = standard deviation of y

[tex]\mu_{x} [/tex] = mean of x

[tex]\mu_{y} [/tex] = mean of y

and, E denotes the Expectation.

The value of the correlation lies between -1 to +1.

If the value of correlation lies between -1 to 0 then it is known as a negative correlation.

and, If the value of correlation lies between 0 to 1 then it is known as a positive correlation.

Using the above formula of correlation we get Correlation (r) = -0.1225.

Thus, there is negative correlation between age and IQ.

We can also use a correlation calculator for getting the value of correlation.

Hence, option (B) is correct.

Answer:

x = -(38/3)

Step-by-step explanation:

Well first you have to isolate the square root on the left hand side.

Then eliminate the radical on the left hand side.

Last step

Solve the linear equation :

Rearranged equation

3x + 38 = 0

Subtract 38 from both sides

3x = -38

Divide both sides by 3

A possible solution is :

x = -(38/3)

For this case we must solve the following equation:

[tex]\sqrt {3x + 54} + 6 = 10[/tex]

Subtracting 6 from both sides of the equation:

[tex]\sqrt {3x + 54} = 10-6\\\sqrt {3x + 54} = 4[/tex]

We square both sides of the equation squared:

[tex]3x + 54 = 4 ^ 2\\3x + 54 = 16[/tex]

We subtract 54 from both sides of the equation:

[tex]3x = 16-54[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]3x = -38[/tex]

We divide between 3 on both sides:

[tex]x = \frac {-38} {3}\\x = - \frac {38} {3}[/tex]

Answer:

[tex]x = - \frac {38} {3}[/tex]

Answer:

x = 8 + 7y

Step-by-step explanation:

Given

x - 7y = 8 ( isolate x by adding 7y to both sides )

x = 8 + 7y

Linear equation is the equation in which the highest power of the unknown variable is one.The value of the variable x for the given expression is,

[tex]x=7y+8[/tex]

The given linear equation is,

[tex]x-7y=8[/tex]

Linear equation is the equation in which the highest power of the unknown variable is one. The linear equation are used to find out the value of unknown variable.

In the above linear equation the coefficient of the variable x is one and the coefficient of the variable y is negative seven.

The number eight is the constant which is equal to the given expression of variables.

To solve the equation for x refers to get the value of the variable x. As there is only one linear equation and the unknown variables are two. Thus the value of variable x can be obtained in the form of the variable y.

Let solve the given equation,

[tex]x-7y=8[/tex]

Add [tex]7y[/tex] both sides of the equation. thus,

[tex]x=8+7y[/tex]

[tex]x=7y+8[/tex]

Thus the value of the variable x for the given expression is,

[tex]x=7y+8[/tex]

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Answer:

[tex]f(2)=\frac{37}{4}[/tex]  or [tex]f(2)=-(-\frac{37}{4})[/tex]

Step-by-step explanation:

we have

[tex]f(x)=2x^{2} +\frac{5}{x+2}[/tex]

Find f(2)

we know that

f(2) is the value of f(x) when the value of x is equal to 2

so

For x=2

substitute

[tex]f(2)=2(2)^{2} +\frac{5}{2+2}[/tex]

[tex]f(2)=8 +\frac{5}{4}[/tex]

[tex]f(2)=\frac{37}{4}[/tex]

or

[tex]f(2)=-(-\frac{37}{4})[/tex]

Answer:

The answer would be 12.8

Step-by-step explanation:

I looked it up and found the answer on another website

it is 12.8

By using the sine rule we got the value of a is 8 units.

Given that, in triangle ABC, angle A = 45, c= 17, and angle B = 25.

We need to find the measure of side a.

The sine rule formula is sinA/a=sinB/b=sinC/c.

Now, sin45°/a=sin25°/b=sin110°/17

⇒sin45°/a=0.9397/17

⇒0.7071/a=0.0854

⇒a=8.27≈8

Therefore, the value of a is 8 units.

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A proportion

[tex]a\div b = c\div d[/tex]

is nothing but a comparison between two fractions: we can rewrite it as

[tex]\dfrac{a}{b}=\dfrac{c}{d}[/tex]

So, we can multiply both sides by the two denominators b and d to get

[tex]\dfrac{a}{b}=\dfrac{c}{d} \iff ad = bc[/tex]

In other words, a proportion is true if the product of the inner terms is the same as the product of the outer terms.

In your case, we have the check is the following:

[tex]24 \div 40 = 4\div 7 \iff 24\cdot 7 = 40\cdot 7 \iff 168 = 280[/tex]

which is clearly false. So, 24:40 = 4:7 is not a true proportion. In fact, if we convert fractions into numbers, we have

[tex]\dfrac{24}{40} = 0.6,\quad \dfrac{4}{7} = 0.\overline{571428}[/tex]

which makes even more clear that the proportion doesn't hold.

Answer:

x is 50 degrees

Step-by-step explanation:

If you subtract 65 twice from 180 you get this answer. The line is a straight line making it equal 180 degrees

The correct answer is 50

Step-by-step explanation:

The first polygon, ABCD, should be rotated around DA' axis and then create a function f'(x)=f(x) +5 to transpose ABCD poligon into A'B'C'D' position

The second polygon, MNOP, rotate around MP axis and half the size ( Area)

Step-by-step explanation:

1b) First, reflect ABCDE over the x-axis.

(x, y) → (x, -y)

Then, translate 5 units to the right and 3 units down.

(x, -y) → (x+5, -y-3)

1c) Instead of reflecting over the x-axis, we can reflect ABCDE over the y-axis.

(x, y) → (-x, y)

Then, rotate about the origin 180 degrees.

(-x, y) → (x, -y)

Finally, translate 5 units to the right and 3 units down.

(x, -y) → (x+5, -y-3)

2b) First, rotate MNOP 90 degrees clockwise about the origin.

(x, y) → (y, -x)

Then, scale by 1/2.

(y, -x) → (y/2, -x/2)

Finally, translate 3.5 units to the left and 2.5 units down.

(y/2 - 3.5, -x/2 - 2.5)

2c) We can form a second method by changing the order of transformations.

First translate MNOP 5 units to the right and 7 units down.

(x, y) → (x + 5, y - 7)

Then scale by 1/2.

(x + 5, y - 7) → (x/2 + 2.5, y/2 - 3.5).

Finally, rotate 90 degrees about the origin.

(y/2 - 3.5, -x/2 - 2.5)

3b) First, rotate EFGH 45 degrees counterclockwise about the origin.

(x, y) → (½√2 (x - y), ½√2 (x + y))

Then scale by ⅓√2.

(½√2 (x - y), ½√2 (x + y)) → (⅓ (x - y), ⅓ (x + y))

Finally, translate 13/3 units to the right and 1 units down.

(⅓ (x - y), ⅓ (x + y)) → (⅓ (x - y) + 13/3, ⅓ (x + y) - 1)

3c) Again, we can form a second method by changing the order of the transformations.

Let's keep the first step the same, rotating EFGH 45 degrees counterclockwise about the origin:

(x, y) → (½√2 (x - y), ½√2 (x + y))

Then translate 13/√2 units to the right and 3/√2 units down.

(½√2 (x - y), ½√2 (x + y)) → (½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2)

Finally, scale by ⅓√2.

(½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2) → (⅓ (x - y) + 13/3, ⅓ (x + y) + 1)

4b) First, rotate XYZ 45 degrees clockwise about the origin.

(x, y) → (½√2 (x + y), ½√2 (y - x))

Then translate 5-√2 units to the right and 4√2 units up.

(½√2 (x + y), ½√2 (y - x)) → (½√2 (x + y) + 5 - √2, ½√2 (y - x) + 4√2)

4c) Instead, let's translate XYZ 5 units to the left and 3 units up.

(x, y) → (x - 5, y + 3)

Then rotate 45 degrees clockwise about the origin:

(x - 5, y + 3) → (½√2 (x + y - 2), ½√2 (y - x + 8))

Finally, translate 5 units to the right.

(½√2 (x + y - 2), ½√2 (y - x + 8)) → (½√2 (x + y - 2) + 5, ½√2 (y - x + 8))

Answer:

The vertex is the point (-5,3)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

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

where

a is a coefficient

(h,k) is the vertex

If a > 0 the parabola open upward and the vertex is a minimum

If a < 0 the parabola open downward and the vertex is a maximum

In this problem we have

[tex]y=2(x+5)^{2}+3[/tex]

a=2

so

the parabola open upward and the vertex is a minimum

h=-5, k=3

therefore

The vertex is the point (-5,3)

Answer: [tex]x=128\°[/tex]

Step-by-step explanation:

It is important to remember the following:

[tex]Angle\ formed\ by\ two\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex]

In this case you can observe in the figure that "x" is an Angle formed by two chords, therefore, you can find its value applying the formula.

Therefore, the value of "x" is this:

[tex]x=\frac{1}{2}(202\°+54\°)\\\\x=\frac{1}{2}(256\°)\\\\x=128\°[/tex]

Answer:

=12 units

Step-by-step explanation:

When a square is cut along one diagonal, it forms a right angled triangle whose legs are the sides of the square and the hypotenuse is the diagonal of the square.

Therefore, the Pythagoras theorem is used to find the hypotenuse.

a² + b² = c²

(6√2)²+(6√2)²=c²

72+72=c²

c²=144

c=√144

=12

The diagonals of the square measure 12 units each.

Answer:

12.5

Step-by-step explanation:

divide 25 by 2

To find the area of the painted part, subtract the area of the missing sector from the area of the entire circle.

The area of the painted part of the figure can be found by subtracting the area of the missing sector from the area of the entire circle. To find the area of the missing sector, we need to know the central angle of the sector. Once we have the central angle, we can use the formula for the area of a sector to calculate the area of the missing sector. Finally, we subtract the area of the missing sector from the area of the entire circle to find the area of the shaded part.

Example:

If the circle has a radius of 5 units and the central angle of the missing sector is 60 degrees, we can calculate:

Area of missing sector = (60/360) * π * 5^2

Area of the shaded part = π * 5^2 - (60/360) * π * 5^2

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Answer:

i) 4π

ii) An isosceles triangle

iii) 8 cm^2[/tex]

iv)  [tex](4\pi - 8)cm^2[/tex]

Step-by-step explanation:

The radius of the circle is 4 cm and the measure of the central angle is 90°.  

We know that the area of sector of a circle = [tex]\frac{central angle}{360} *\pi *r^2[/tex]

Given: r = 4 and central angle = 90

Now plug in these values in the above formula, we get

Area of the sector = [tex]\frac{90}{360} *\pi *4^2\\= \frac{1}{4} *\pi *16\\= 4\pi[/tex]

i) 4π

ii) In the triangle, the two sides are equal in measure, because the two sides represents the radius of the circle. The radius are the same in measure in a circle.

Therefore, the triangle is the second is an isosceles triangle.

iii) Area of a right triangle = [tex]\frac{1}{2} *base*height[/tex]

Here base = 4 and height = 4, plug in these values in the triangle formula, we get

The area of the triangle = [tex]\frac{1}{2} *4*4\\= 2*4\\= 8 cm^2[/tex]

iv) The area of the segment of the circle is (4π - area of the triangle).

= [tex](4\pi - 8)cm^2[/tex]

The area of a sector is calculated using:

[tex]A = \frac{\theta}{360} \times \pi r^2[/tex]

So, we have:

[tex]A = \frac{90}{360} \times \pi \times 4^2[/tex]

[tex]A = \frac{1}{4} \times \pi \times 4^2[/tex]

[tex]A = 4\pi[/tex]

Hence, the area of the sector is [tex]4\pi[/tex]

One of the angles in the triangle is 90 degrees.

So, the triangle is a right-angled triangle

The area of the triangle is then calculated as:

[tex]A = \frac 12 bh[/tex]

This gives

[tex]A = \frac 12 \times 4 \times 4[/tex]

[tex]A = 8[/tex]

Hence, the area of the triangle is 8, and the triangle is a right triangle

This is the difference between the areas of the circle and the triangle.

So, we have:

[tex]A = 4\pi - 8[/tex]

Hence, the area of the segment is [tex] 4\pi - 8[/tex]

Read more about areas at:

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Answer:

There are 32 words total on the list.

Step-by-step explanation:

24*4=96;  

96÷3=32;  

There are 32 words total on the list.

Answer:

gfrwkmsvfbs

Step-by-step explanation:

dfffve

Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

THe most common mistake would be to think 1/4th of the kites flew, BUT 1/4th of the trapezoidal kites flew.

Hence, 1/4th of 8/9th of the TOTAL KITES FLEW, that is:

[tex]\frac{1}{4}*\frac{8}{9}=\frac{2}{9}[/tex]

hence, 2/9th of the kites flew

Answer:

12

Step-by-step explanation:

The number 144 can be factorized as = 2*2*2*2*3*3= (4^2)* (3^2)

Therefore, sqrt(144)= sqrt((4^2)* (3^2))= sqrt{(4*3)^2= sqrt{12^2}=12

Answer:

270 7/16 in^2.

Step-by-step explanation:

The surface area equals the sum of the  areas of 3 pairs of congruent rectangles.

These are  2 * 8 * 1 3/4 + 2 * 8 * 12 1/2 + 2 * 1 3/4 * 12 / 1/8

= 16 * 7/4  +  16 * 25/2 + 2 * 7/4 * 97/8

=  28 + 200 + 42 7/16

= 270 7/16 in^2.

Answer:

Option B k > 0

Step-by-step explanation:

we know that

Observing the graph

The slope of the line is positive

The y-intercept is negative

we have

[tex]3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)[/tex]

The slope of the line is equal to

[tex]m=\frac{1}{3}[5k+2][/tex]

Remember that the slope must be positive

so

[tex]5k+2> 0\\ \\k > -\frac{2}{5}[/tex]

The value of k is greater than -2/5

Analyze the y-intercept

[tex](2-\frac{4}{3}k) < 0\\ \\ 2 < \frac{4}{3}k\\ \\1.5 < k\\ \\k > 1.5[/tex]

1.5 is greater than zero

so

the solution for k is the interval ------> (1.5,∞)

therefore

must be true

k > 0