I solved the first one but I can’t figure out the second one

To find the area of the triangle with vertices (9,-1), (6,1), and (6,3), we can use the formula:

\($A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$\)

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices.

Plugging in the coordinates, we get:

\($A = \frac{1}{2} \left| 9(1-3) + 6(3-(-1)) + 6((-1)-1) \right|$\)

\($A = \frac{1}{2} \left| -6 + 24 - 12 \right| = \frac{1}{2} \cdot 6 = 3$\)

Therefore, the area of the triangle is 3 square units.

To find the area of the triangle with vertices (0,-8), (0,-10), and (7,-10), we can again use the formula:

\($A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$\)

Plugging in the coordinates, we get:

\($A = \frac{1}{2} \left| 0((-10)-(-10)) + 0((7)-0) + 7((-8)-(-10)) \right|$\)

$A = \frac{1}{2} \cdot 14 = 7$

Therefore, the area of the triangle is 7 square units.

To find the area of the triangle with vertices (6,-7), (3,-1), and (-1,4), we can again use the formula:

\($A = \frac{1}{2} \left| x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) \right|$\)

Plugging in the coordinates, we get:

\($A = \frac{1}{2} \left| 6((-1)-4) + 3(4-(-7)) + (-1)((-7)-(-1)) \right|$\)\($A = \frac{1}{2} \cdot 55 = \frac{55}{2}$\)

Therefore, the area of the triangle is $\frac{55}{2}$ square units.

To find the area of the quadrilateral with vertices (-6,1), (-9,1), (-6,-4), and (-9,-4), we can divide it into two triangles and find the area of each triangle using the determinant method. The area of the quadrilateral is the sum of the areas of the two triangles.

First, we find the coordinates of the diagonals:

$D_1=(-6,1)$ and $D_2=(-9,-4)$

The area of the quadrilateral can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} -6 & 1 \ -9 & -4 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -9 & -4 \ -6 & -4 \end{array}\right|\

&=\frac{1}{2}\cdot 21 + \frac{1}{2}\cdot 9\

&=\frac{15}{2}\

\end{align*}

Therefore, the area of the quadrilateral is $\frac{15}{2}$ square units.

To find the area of the pentagon with vertices (0,3), (-3,3), (-5,1), (-3,-3), and (-1,-2), we can divide it into three triangles and find the area of each triangle using the determinant method. The area of the pentagon is the sum of the areas of the three triangles.

First, we find the coordinates of the diagonals:

$D_1=(0,3)$ and $D_2=(-1,-2)$

The area of the pentagon can be calculated as:

\begin{align*}

\text{Area}&=\frac{1}{2}\left|\begin{array}{cc} x_1 & y_1 \ x_2 & y_2 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_2 & y_2 \ x_3 & y_3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} x_3 & y_3 \ x_4 & y_4 \end{array}\right|\

&=\frac{1}{2}\left|\begin{array}{cc} 0 & 3 \ -3 & 3 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -3 & 3 \ -5 & 1 \end{array}\right| + \frac{1}{2}\left|\begin{array}{cc} -5 & 1 \ -3 & -3 \end{array}\right|\

&=\frac{1}{2}\cdot 9 + \frac{1}{2}\cdot (-6) + \frac{1}{2}\cdot (-8)\

&=\frac{5}{2}\

\end{align*}

Therefore, the area of the pentagon is $\frac{5}{2}$ square units.

Area of triangle whose vertices are (6,1), (9,-1) and (6,-3) is 6 square units and the area of triangle whose vertices are (0,-8), (7,-10) and (0,-10) is 7 square units.

A polygon having 3 edges and 3 vertices is called a triangle. It is one of the fundamental geometric forms.

Lets find the area of triangle ( Pink Colour) whose vertices are (6,1), (9,-1) and (6,-3), \(Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ]\)

Area = 1/2 [ 6 ( -1 - (-3) ) + 9( -3 -1 ) + 6( 1 - ( -1 ) ) ]

Area = 1/2 [6 * 2 + 9 * (-4) + 6 * 2]

Area = 1/2 [12-36+12] = 1/2 (-12) = -6

Therefore , Area of Triangle is 6 square units.

Now, Lets find the area of triangle ( Brown Colour ) whose vertices are (0,-8), (7,-10) and (0,-10),

\(Area = \frac{1}{2} [x_{1}(y_{2} -y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2} ) ]\)

Area = 1/2 [  0( -10 - ( -10 )) + 7 ( -10 - ( -8 ) ) + 0 ( -8 - ( -1- ) ) ]

Area = 1/2 [ 0 + 7 * (-2) + 0]

Area = 1/2 ( -14 ) = -7

Therefore, Area of Triangle is 7 square units.

Now. Lets find the area of Rectangle( Blue Colour ) whose length is 5 unit and Breadth is 3 unit.

So, Area of Rectangle = Length * Breadth

= 5 * 3 square units

= 15 square units.

To Learn more about Triangle, visit:

https://brainly.com/question/1058720

#SPJ1

Answer:

  $700 for a chair and a table

Step-by-step explanation:

Let t and c represent the price of a table and a chair, respectively. The given relations are ...

  10c = 4t

  15c +2t = $4000

Divide the first equation by 2 and substitute for 2t:

  5c = 2t

  15c +5c = $4000

  20c = $4000

  c = $200

  t = 5c/2 = 5($200)/2 = $500

The total price of a chair and a table is ...

  $200 +500 = $700 . . . . price of a chair and a table

The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

To know more about hypotenuse:

https://brainly.com/question/12006293

#SPJ1

Answer:

75.27

Step-by-step explanation:

Rectangle = 20+2+2+20-11=47

quarter circle = 1/4(2)(11)(3.14)=17.27 + 11 = 28.27

47+28.27=75.27

Answer:

75.27.cm

Step-by-step explanation:

it works i got a 100 on the test

Answer: The mean is 3780

Step-by-step explanation:

Mean is found by adding all values and dividing the sum by how many values were added.

4250+4019+3895+3739+3401+3376=22680
22680/6=3780

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

\(\frac{-2.2}{6.1}\)

Step-by-step explanation:

If you use the slope formula:

and you plug everything in you will get -2.2/6.1

Answer:

\(\frac{-2.2}{6.1}\)

Answer:2\(\sqrt{6}\)because it is a 45 45 90

Step-by-step explanation:

On solving the provided question, we can say that - the range \(|x + 1| = 0\) \(x + 1 = 0 = > x = -1\) and \(y = 3\)

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

\(|x + 1| = 0\\x + 1 = 0\\x = -1\)

\(y = |-1 + 1| + 3\\y= 0 + 3\\y = 3\)

To know more about range visit:

https://brainly.com/question/28135761

#SPJ1

Answer:

3. 7kg

4. 100kg

5. 13kg more

6. $64

7. 200kg

Answer:

$26

Step-by-step explanation:

15 * 2= 30

30-4= 26

To reach their financial objective of having $130,000 accessible for their child's schooling when the youngster turns 18, the parents must set aside roughly $97,209.87 at 3% compound semiannually.

To determine how much money needs to be set aside to meet the financial goal of $130,000 for the child's education, we can use the compound interest formula:

\(A = P(1 + r/n)^(nt)\)

where A represents the future value, P represents the principal (or initial investment), r represents the annual interest rate, n is the frequency with which interest is compounded annually, and t represents the passage of time in years.

To solve for the principal, P, in this situation, we must first identify the principal, P.

\(P = A / (1 + r/n)^(nt)\)

Given that the child is currently 10 years old and will need the money in 8 years (at age 18), we have t = 8. The interest rate is 3%, which we need to express as a decimal (r = 0.03), and the interest is compounded semiannually, so n = 2.

Using these values and the desired future value of $130,000, we can calculate the required principal:

P = \(130000 / (1 + 0.03/2)^(2*8)\) = $97,209.87

Learn more about compound here:

https://brainly.com/question/28792777

#SPJ1

Answer:

b

Step-by-step explanation:

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

Learn more on length : https://brainly.com/question/23008020

#SPJ1

Answer:

1244 DCD

Step-by-step explanation:

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Reflection over the line x = -1 alters the x-coordinates, but leaves the y-coordinates alone. The image point is as far horizontally from the reflection line as the pre-image point is.

Each new x-coordinate is the old one subtracted from twice the x-value of the line of reflection:

  (x, y) ⇒ (-2-x, y)

  U(-8, -6) ⇒ U'(6, -6)

  V(-3, -6) ⇒ V'(1, -6)

  W(-4, -1) ⇒ W'(2, -1)

Answer:

The expression is equivalent to  \(-4\cdot x^{2}+3\cdot x -5\).

Step-by-step explanation:

In this exercise we must transform \(-4\cdot x^{2}+2\cdot x -5\cdot (1+x)\) into its standard form, that is a polynomial of the form:

\(y = a\cdot x^{2} + b\cdot x + c\) (1)

Where:

\(y\) - Dependent variable.

\(x\) - Independent variable.

\(a\), \(b\), \(c\) - Coefficients.

Let \(y = -4\cdot x^{2}+2\cdot x -5\cdot (1+x)\), now we proceed to convert it into its standard form:

1) \(-4\cdot x^{2}+2\cdot x -5\cdot (1+x)\) Given

2) \((-4)\cdot x^{2}+2\cdot x + (-5)\cdot (1+x)\) \((-a)\cdot b = -a\cdot b\)

3) \((-4)\cdot x^{2}+2\cdot x +(-5)\cdot 1 +(-5)\cdot x\) Distributive property

4) \((-4)\cdot x^{2}+[5+(-2)]\cdot x -5\) \((-a)\cdot b = -a\cdot b\)/Commutative and distributive properties

5) \(-4\cdot x^{2}+3\cdot x -5\) \((-a)\cdot b = -a\cdot b\)/Definition of subtraction/Result

The expression is equivalent to  \(-4\cdot x^{2}+3\cdot x -5\).

Answer:

Box 1 = -4

Box 2 = -3

Box 3 = -5

Step-by-step explanation:

Plato/Edmentum

Step-by-step explanation:

we have 2 probabilities :

1. that a driver is wearing their safety belts : 0.68

2. that the driver is NOT wearing the safety belts :

1-0.68 = 0.32

A.

3 drivers are wearing it, 2 are not is a combination of

0.68³×0.32²

and how many combinations of these 5 probabilities can we have (e.g. the first 3 are wearing them, or the last 3 are wearing them, or ...) ?

that is 5 over 3 combinations :

5! / (3! × (5-3)!) = 5! / (3! × 2!) = 5×4/2 = 5×2 = 10

so, we have

10×0.68³×0.32² = 0.321978368

B

I am not sure I understand the question.

I assume this means from the 5 drivers they pull over the first 4 don't wear the seat belts, and only the fifth does.

so that is then

0.32⁴×0.68

and only one combination is possible. so, the result is just the product of these probabilities :

0.32⁴×0.68 = 0.0071303168

Answer:

y=60

Step-by-step explanation:

Answer:

93.684

Step-by-step explanation:

They just give a 5% bonus to the price of the lunch

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer: Question one:
              a) 6.67 boxes/ hour
              b) 10 boxes/ hour
              c) 3.33 boxes/ hour
              d) 49.93% increase

Step-by-step explanation:

Question two:

a) 33.33 valves/ hour
b) 36.67 valves/ hour
c) 10.02% increase

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

For more such questions on Intersection, click on:

https://brainly.com/question/30915785

#SPJ8

Answer:

The cost of one share of the stock on Friday is $41.45

Step-by-step explanation:

The initial cost of one share of the stock on Monday is $41.45.

On Tuesday, the cost goes up by $0.58, so the cost becomes:

$41.45 + $0.58 = $42.03

On Wednesday, the cost goes down by $0.26, so the cost becomes:

$42.03 - $0.26 = $41.77

On Thursday, the cost also goes down by $0.26, so the cost becomes:

$41.77 - $0.26 = $41.51

Finally, on Friday, the cost goes down by $0.06.

So the expression to represent the cost of one share of the stock on Friday is:

$41.51 - $0.06

To evaluate this expression, we simply subtract $0.06 from $41.51:

$41.51 - $0.06 = $41.45

Therefore, the cost of one share of the stock on Friday is $41.45

Answer:

D. 270 cm2

Step-by-step explanation:

2*(15*5 + 15*3 + 5*3) = 270 cm2

Answer: x=0

Step-by-step explanation:

2x-x=0

Move the variable to the left-hand side and change its sign

2x-x=0

Collect like terms

X=0

Answer:

Is that 11/3 because of rise over run??? I'm not sure

Let's create a simple proportion.

p = Percent

p/100 = 106/438

Now, cross multiply.

438p = 10,600

Divide both sides by 438 to isolate p.

p ≈ 24.200913242

Therefore, 106 is approximately 24.201 percent of 438.

106 is 24% of 438.

A relative value indicating hundredth parts of any quantity.

Given that, a number 438

Let p be the percent,

p% of 438 = 106

p = 106*100/438

p = 24%

Hence, 106 is 24% of 438.

For more references on percentage, click;

https://brainly.com/question/29306119

#SPJ2