1.complete the column of proof

given < B=<D, m<b=80
prove <c=100
2.complete the paragraph proof
GIVEN<a  a=and <b are complementary and <b  and <c are complementary proof <a =<c

Givens

m<T = 120

m<C = 30

PC = 4

Find PC

Solution

4/sin(30) = PC / sin(120)         Note: this is the sine law.

Multiply both sides by sin(120)

[tex]\dfrac{4*sin(120)}{sin(30)} = \text{PC}[/tex]

4*0.866/0.5 = PC

Answer

PC= 6.928

To find the amount Mrs. Palmer originally had to spend on each daughter, we set up the equation as (x - 18) / 3 = y, where x is the total money she initially had and y indicates the amount spent on each daughter.

Let's denote the total amount Mrs. Palmer originally had as x.

We know she spent this on buying swimming items for her three daughters and had $18 left afterwards.

This infers that the total money she spent is (x - 18) dollars.

Since each daughter received a pair of goggles, a bathing suit, and a beach towel, this means she used this money to buy three sets of swimming items.

Therefore, the amount of money she spent on each daughter is equal to (x - 18)/3.

The equation to find out what x (the amount Mrs. Palmer originally had) is therefore:

(x - 18) / 3 = y

where y represents the amount she spends on each daughter.

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if im not mastaken the answer is -48

Let's form the difference of the two expressions and see what we can learn.

(2y -x) -(2x -y) = 2y -x -2x +y = 3y -3x = 3(y -x)

Since y > x, this is positive, so 2y -x is greater than 2x -y.

If the angle is 90 degrees, then the complement would be 27, because 90 / 3 = 30, and 30 - 3 = 27. Basically, you divide the angle by 3 and subtract 3 to find the complement if this is the case.

Answer:

22⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Given:

x = 3 (90 - x) + 2

x = 270 - 3x + 2

4x = 272

x = 68

Complement = 90 - 68 = 22⁰

(1) QS bisecting <PQR implies <PQS = <SQR

(2) <PQS=45 deg and (1) imply <SQR also = 45 deg

(3) from (2) it follows that <PQR = <PQS + <SQR = 45 + 45 deg = 90 deg and therefore the triangle is right-angled

- 9 ≤ x ≤ 7

the domain is the values of x on the x- axis that define y = f(x)

y is defined for all values of x in the stated domain

N = 10.79

isolate N by adding 6.47 to both sides of the equation

N = 4.32 + 6.47 = 10.79

The unknown number N in the equation N - 6.47 = 4.32 is found to be 10.79 when we add 6.47 to both sides of the equation.

To solve for the unknown number N in the equation N - 6.47 = 4.32, we must isolate the variable N on one side of the equation. We do this by adding 6.47 to both sides of the equation:

N - 6.47 + 6.47 = 4.32 + 6.47

This simplifies to:

N = 10.79

The unknown number N is therefore 10.79. When providing the final answer, we must make sure that it is reported with the correct number of significant figures, which in this case are three significant figures.

ONE solution was found, 1.5

IQR = 6

First locate the median [tex]Q_{2}[/tex] at the centre of the data arranged in ascending order. Then locate the lower and upper quartiles [tex]Q_{1}[/tex] and [tex]Q_{3}[/tex] located at the centre of the data to the left and right of the median.

Note that if any of the above are not whole values then they are the average of the values either side of the centre.

rearrange data in ascending order

15 16 ↓17 17 18 21 22 ↓23 25

                     ↑

[tex]Q_{2}[/tex] = 18

[tex]Q_{1}[/tex] = [tex]\frac{16+17}{2}[/tex] = 16.5

[tex]Q_{3}[/tex] = [tex]\frac{22+23}{2}[/tex] = 22.5

IQR = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 22.5 - 16.5 = 6

Final answer:

The interquartile range (IQR) for the given data set is calculated by first arranging the data in ascending order, finding the first and third quartiles (Q1 and Q3), and subtracting Q1 from Q3. The correct IQR for this data set, following this methodology, is 6, not the mistakenly provided 7.

Explanation:

The question asks about calculating the interquartile range (IQR) of a given data set. The IQR is important because it measures the middle 50% spread of data, pinpointing where the bulk of values lie, and helps in identifying potential outliers. To compute the IQR, we first need to organize the data in ascending order, then find the first quartile (Q1) and the third quartile (Q3), and finally subtract Q1 from Q3 (IQR = Q3 - Q1).

For the provided data set: 17, 16, 21, 15, 25, 22, 18, 23, 17:

Arrange data in ascending order: 15, 16, 17, 17, 18, 21, 22, 23, 25.

Find the median (Q2), which is 18 in this case as it's the middle value.

Q1 is the median of the first half (excluding the middle value if odd number of data), so Q1 = 16.5.

Q3 is the median of the second half, hence Q3 = 22.5.

Therefore, IQR = Q3 - Q1 = 22.5 - 16.5 = 6.

Contrary to the mistaken calculation of IQR as 9 - 2 = 7 provided in the reference, the computed IQR for this data set, following the correct methodology, is 6.

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

for (0,3): 3 = -0 + 3  good

for (4,-1): -1 = -4 + 3  good

(c)

Substitute the x-coordinate from each point into the equation and if equal to the corresponding y- coordinate then the point lies on the line

(a)

x = - 1 : y = 1 + 3 = 4 ≠ - 2

x = 1 : y = - 1 + 3 = 2 ≠ 4

(b)

x = 1 : y = 2 = 2

x = 0 : y = 0 + 3 = 3 ≠ - 3

(c)

x = 0 : y = 3 = 3 ← correct

x = 4 : y = - 4 + 3 = - 1 = - 1 ← correct

the pair of points is (c)

Mrs. Riley can make 168 pillows because she bought 168.75 yards of fabric and each pillow requires 1 yard of fabric.

First, we need to determine how many yards of fabric Mrs. Riley purchased. We do this by dividing the total cost of the fabric ($405) by the cost per yard ($2.40). So, 405 ÷ 2.4 = 168.75 yards. Each pillow requires 1 yard of fabric, therefore she can sew 168 pillows with no leftover fabric.

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Answer:

Total gallons of fresh water in the tank [tex]3.1926*10^3[/tex] gallons.

Step-by-step explanation:

Percentage of fresh water = [tex]100%-6.1%[/tex]

                                            =93.9%

Total number of gallons of water in tank = [tex]3.4*10^3[/tex]   (given in the question)

Therefore,

Total gallons of fresh water in the tank   =  [tex]3.4*10^3*93.9/100[/tex]

                                                                  =[tex]3.1926*10^3[/tex] gallons.

Answer:

6i\sqrt{19}

Step-by-step explanation:

If you want to simplify this, you can add the coefficients of like terms.

... = x²(2+2) +x(4+4) +(-3-3)

... = 4x² +8x -6

_____

Since both of the parts of the sum are the same, this expression can be rewritten using the distributive property:

... = 2(2x² +4x =3)

_____

The sum can also be rewritten to vertex form.

... = 4(x² +2x) -6

... = 4(x² +2x +1) -6 -4(1)

... = 4(x +1)² -10

This is an expression describing a parabola with vertex (-1, -10) and a vertical scale factor of 4. It has roots (x-intercepts) at -1±√2.5.

8000 because u add an extra 0 if u multiple with a number with a zero or no

The price of the small pots is $2.40 so you would have 2.4s ( multiply the number of small pots by the price)

She bought a total of 14 pots, so the number of large pots would be 14 - s ( subtract the number of small pots from the total )

Now you have:

L = 14-s

2.4s + 5.6(14-s) = 49.6

The answer is C.

Divide 50 by 22: 2.27272727...

Round up to hundredth and your final answer is 2.27

hope that helps :)

Your identity says ...

... sum of cubes = (sum)³ -3(product)(sum)

... = 4³ -3·1·4

... = 64 -12 = 52

_____

The two numbers are 2±√3, and the sum of their cubes is indeed 52.

To find the answer,we need to first find the legth of the not given side of triangle by using Pythagoras theorem:

[tex] = \sqrt{{15 }^{2} -{ 9 }^{2} } \\ = \sqrt{144 }\\ = 12[/tex]

Therefore the side length is 12in.

Therefore the answer 12 in.

The total height of the stair is equivalent to 36 inches.

Pythagoras theorem states that the square of the hypotenuse is equivalent to the square of the base and perpendicular.

We can write the formula for Pythagoras theorem as -

(hypotenuse)² = (base)² + (perpendicular)²

We can write the height of the stairs as -

h = 3 x √(15² - 9²)

h = 3 x √(225 - 81)

h = 3 x √144

h = 3 x 12

h = 36 inches

Therefore, the total height of the stair is equivalent to 36 inches.

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The equation of the circle in standard form with a center at (2, -3) and a radius [tex]\(4\sqrt{5}\)[/tex] is [tex]\( (x - 2)^2 + (y + 3)^2 = 80 \)[/tex].

To find the equation of the circle with the diameter endpoints given,

The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula:

Midpoint [tex]\((M_x, M_y)[/tex] = [tex]\left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)\)[/tex]

For the endpoints A (-2,-5) and B (6,-1), we calculate:

[tex]\(M_x = \frac{-2 + 6}{2} = \frac{4}{2} = 2\)[/tex]
[tex]\(M_y = \frac{-5 + (-1)}{2} = \frac{-6}{2} = -3\)[/tex]

So, the midpoint, which is the center of the circle, is C (2, -3).

The radius is half the length of the diameter, and the length of the diameter is the distance between the endpoints A and B using the distance formula:

Distance d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2} \)[/tex]

r = [tex]\frac{d}{2} = \frac{\sqrt{(6 - (-2))^2 + (-1 - (-5))^2}}{2} \)[/tex]

Calculating the expressions:

r = [tex]\frac{\sqrt{(6 + 2)^2 + (-1 + 5)^2}}{2} \)[/tex]
 = [tex]\frac{\sqrt{8^2 + 4^2}}{2} \)[/tex]
 = [tex]\frac{\sqrt{64 + 16}}{2} \)[/tex]
 = [tex]\frac{\sqrt{80}}{2} \)[/tex]
 = [tex]\frac{8\sqrt{5}}{2} \)[/tex]

r = [tex]4\sqrt{5} \)[/tex]

The equation of a circle with center (h, k) and radius r can be represented as:
[tex]\( (x - h)^2 + (y - k)^2 = r^2 \)[/tex]

Plugging our midpoint as the center and our radius into the equation:

[tex]\( (x - 2)^2 + (y + 3)^2 = (4\sqrt{5})^2 \)[/tex]

Simplifying,
[tex]\( (x - 2)^2 + (y + 3)^2 = 16 \cdot 5 \)[/tex]
[tex]\( (x - 2)^2 + (y + 3)^2 = 80 \)[/tex]

Thus, the required equation is [tex]\( (x - 2)^2 + (y + 3)^2 = 80[/tex].

Answer:

The last quiz score must be at least an 80 to get the average to be a 70.

Step-by-step explanation:

In order to find this, you need to take the average of the 4 test scores along with the unknown test score (x). So, to find an average, we add all the numbers together and divide by the amount of tests taken. We can then set this equal to 70 since that is the minimum average.

(60 + 64 + 75 + 71 + x)/5 = 70 ------> Multiply both sides by 5

(60 + 64 + 75 + 71 + x) = 350 -----> Combine like terms

270 + x = 350 -----> Subtract 270 from both sides

x = 80

30

dividing the length and width by 2

10 ÷ 2 = 5 and 12 ÷ 2 = 6

he can plant 5 × 6 = 30 pumpkin plants

Assuming the adults that have children and the ones that don't together make up the entire population of adults, then the number that have children will be ...

... 4200 - (3/8)×4200

... = 4200×(1 -3/8) = 4200×5/8 = 2625

2625 adults in Lakeview have children

9514 1404 393

Answer:

  25% increase

Step-by-step explanation:

A percentage change is calculated using the formula ...

  percent change = ((new value) - (old value))/(old value) × 100%

  = (500 -400)/400 × 100%

  = 100/400 × 100%

  = 25%

A positive percentage change indicates an increase.

The change from 400 to 500 is a 25% increase.

Answer: C

Step-by-step explanation:

Answer:

OPtion C is correct answer.

Step-by-step explanation:

Given that there is a system of equations as

y =-4x+3 and y =3x+1

Table is prepared with side by side values of y for a given x

From the table we are to find the solution of the system

On analysing the table we find that the difference between two y's is

0.5, -0.2, -0.9, -1.6, -2.3,-3

Hence we select the one which shows minimum difference i.e. -0.2

For this, x = 0.6

When x =0.6, y shows two values as 0.6 and 0.8

So we approximate y value as average of these two i.e. 0.7

So solution is

(0.6, 0.7)

daniel will be 32 and his son will be 8

To find the number of boys, you can set up an equation using the given information. Solve the equation to find the number of boys.

To solve this problem, let's define a variable for the number of boys. Let x represent the number of boys.

According to the problem, we know that the amount of boys is 3 times the number of boys, minus 2. So the expression for the number of boys is 3x - 2.

We also know that the total number of people is 26. Therefore, we can set up an equation: 3x - 2 + x = 26.

By combining like terms and solving the equation, we can find the number of boys. The solution is x = 7. Therefore, there are 7 boys.

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Answer:

Option C is right answer

Step-by-step explanation:

We have in coordinate geometry a straight line in slope intercept form as

y = mx+c

where m is the slope and c is the y intercept

There are special lines when m=0 and m = infinity.

When a line is parallel to y axis, it has slope = tan90 = infinity.

Hence line will have equation of the form x = a for some a.

Since the line passes through (3,2) we can find a using this.

Substitute x value to get 3 = x

Hence equation of the line is x =3

Answer:

X=3

Step-by-step explanation:

The primes in the range 1–38 are ...

... 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

There are 12 of them, so the probability of drawing a prime is

... 12/38 = 6/19

Answer:

[tex]\text{Probability}=\frac{6}{19}[/tex]      

Step-by-step explanation:

Given : Balls numbered from 1 to 38 are placed in a container and stirred. If one is drawn at random.

To find : The probability that the number is a prime number

Solution :  

Probability is defined by,

[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]

Favorable outcomes - To get the number is prime number from 1 to 38

Prime numbers are those which were not divisble by any number except 1 and itself.

From 1 to 38 - 2,3,5,7,11,13,17,19,23,29,31,37

Favorable outcome = 12

Total number of outcome is 1 to 38 = 38

[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]

[tex]\text{Probability}=\frac{12}{38}[/tex]

[tex]\text{Probability}=\frac{6}{19}[/tex]