The sum of two numbers is 56. The difference between the two numbers is 12. What are the two numbers?

Question 11

1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)

4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)

Question 12

1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)

2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)

4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)

5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)

6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)

7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)

Note: I changed the names of the segments in Question 11 because of the word filter.

The line plot shown C in the figure is correct.

Given that the recorded lengths of ribbon pieces which is used in project is [tex]11\frac{1}{4},11\frac{1}{4},10\frac{3}{4},10\frac{1}{2},10\frac{7}{8},10\frac{5}{8},9\frac{7}{8},11\frac{1}{4}[/tex].

Frequency refers to the number of times an event or  value occurs. A frequency table is a table that lists items and shows how many times those items occurred.

A line plot displays the data using a no. line.

Firstly, we will fimd the frequency of each value

Values                               Frequency

9 (7/8)                                        1

10(4/8)=10(1/2)                           1

10(5/8)                                       1

10(6/8)=10(3/4)                          1

10(7/8)                                       1

11(2/8)=11(1/4)                             3

Option A is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)

Option B is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)

Option C is correct because the frequency distribution of the data is represented correctly in the line plot.

Option D is incorrect because 11(2/8) has 2 data values in the line plot (i.e., frequency = 2)

Hence, the line plot which correct shows the data is third line plot.

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Using sampling concepts, it is found that:

a) The best method is: 25 adult residents are randomly selected from the city;

b) The estimate is that 11,536 adults voted in the election.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

In this problem, the sample will be representative if all adults, no matter if senior or not, homeowners or not are represented, hence the best method is:

25 adult residents are randomly selected from the city;

The estimate of the number of adults that voted is:

14/25 x 20,600 = 11,536.

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Answer:

X-19

Step-by-step explanation:

First you need to distribute the three into the numbers in the parenthesis,

(3 * x) + (3  * -5) - (2x + 4)

That then turns into,

3x - 15 - (2x + 4)

but we aren't done distributing yet, because the second set of parenthesis has a negative sign in front of it we also have to distribute that. (this is because the negative sign is really just -1)

3x - 15 + (-1 * 2x) + (-1 * 4)

that turns into,

3x - 15 - 2x -4

from here all we have to do is add like terms,

(3x - 2x) + (-15 + -4)

and that leaves us with: 1x -19 or x-19

Hope that helped :))  

c2 =a2 +b2

that's the rule

for example

c2=5^2+5^2

c2=25+25

c2=50 square root is

c=7.07^2

Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

In this problem, the parameters are:

a = 800, b = 900, C = 70º.

Hence the distance across the lake is c, found as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

c² = 800² + 900² - 2(800)(900)cos(70º)

c² = 957491

[tex]c = \sqrt{957491}[/tex]

c = 978.5.

The distance across the lake is of 978.5 feet.

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Answer:

300 dollars

Step-by-step explanation:

Note that:

{Peter's revenue on Monday: 150 dollars

Peter's revenue on Tuesday: 100 dollars

Peter's revenue on Wednesday: 50 dollars}

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

In this problem, we need to find how much is Peter's revenue so far (total).

We need to use addition to determine how much Peter's revenue is in total.

So, add 150, 100, and 50.

We get 150 + 100 + 50 = 300

Finally, Peter's revenue in total is 300 dollars.

Answer:

$300

Step-by-step explanation:

add 150+100+50

=300

Based on the graph of the function (F(x) = log6x), the following facts are true:

A graph is a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.

By critically observing the graph of the function (F(x) = log6x) attached in the image below, we can infer and logically deduce that its domain and range include all real numbers that are greater than 0 (x > 0).

This ultimately implies that, the following facts are true:

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Complete Question:

Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x

A. It is increasing.

B. The range is y > 0.

C. The x-intercept is (1, 0).

D. It is decreasing.

E. The y-intercept is (0, 6).

F. The domain is x > 6.

Answer:

Step-by-step explanation:

If the lines are parallel, it means that the slopes are the same.  To write an equation in the slope intercept form, we need the slope and the y-intercept.  We are given the slope.  We need to find the y-intercept.  We can use the slope and the point to help us.  The point is written in the form (x,y).  In this case the point is (2,4) so we will use 2 for x and 4 for y.

y = mx + b  Plug in what we know

4 = -4(2) + b  b is what we are looking for.  It is the y-intercept

4 = -8 + b  Now add 8 to both sides

12 = b

Now we can write the equation:

y = -4x +12

The  sum of the links of the two parallel sides is 5cm

The formula for calculating the area of a trapezoid is expressed as:

A = 0.5(a+b)h

where

h is the height of the trapezoid

a+b is the sum of the sides

Substitute

20 = 0.5(a+b)8

40 = 8(a+b)

a+b = 40/8

a+b = 5cm

Hence the  sum of the links of the two parallel sides is 5cm

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming the equation is:}[/tex]

[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]

[tex]\huge\textbf{If so, let's start simplifying it:}[/tex]

[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]

[tex]\mathsf{= (12.3\times 12.3) - (0.246 \div 3)}[/tex]

[tex]\mathsf{= (151.29) - (0.246 \div 3)}[/tex]

[tex]\mathsf{= 151.29 - 0.246 \div3}[/tex]

[tex]\mathsf{= 151.29 - 0.082}[/tex]

[tex]\mathsf{= 151.208}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\large\boxed{\mathsf{Exactly \rightarrow} \frak{\ 151.208\ } \& \textsf{ Corrected to two significant figures}\rightarrow \frak{150 \ or \ 151}}\large\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

60

Step-by-step explanation:

140 = 80 + z

z = 60

Answer:

60°

Step-by-step explanation:

The whole angle is 140° and one side is 80°. Now, you just have to subtract 140 and 80 to get 60. I hope this helps!

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (f + g)(x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: f(x) + g(x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)[/tex]

[tex]\qquad \sf  \dashrightarrow \: 7 {x}^{2} + x - 4[/tex]

The height of the basketball hoop to the nearest foot will be 12ft .

There are two ways to continue. The first method is to use trigonometric ratios.

You can use the tangent ratio because you have specified one leg and are trying to solve it with the other leg.

x equals the length of the other leg. .. Plug in known values.

Another way to find out is to monitor the angle. If the two angles are 45 degrees and 90 degrees, you can see that the third angle is 45 degrees. This makes it an isosceles triangle. That is, the other leg is 7 feet long.

2) Determine the height of the tire

Add 7 feet and 5 feet (human height):

7 + 5 = 12 feet

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Answer:

i need this too hahahaha

The values when the given numbers are multiplied will be:

230

78

3

91

1800

3. 5 × 23 × 2

It should be noted that the given information simply means that we should multiply 5 by 23 by 2. This will be:

= 5 × 23 × 2

= 230

5. 34 + 0 + 18 + 26

This information simply means that we should add thirty four, eighteen, and twenty six together. This will be:

34 + 0 + 18 + 26 = 78

7. (3 × 10 × 8) = ....... × (10 × 8)

(3 × 10 × 8) = 3 × (10 × 8)

9. 0 + ...... = 91

It simply means the number that will be added to zero that will give ninety one. This will be 91.

11. The total income for the theater will be:

= (20 × 18) × 5

= 1800

Therefore, the correct values based on the computation will be 730, 78, 3, 91, and 1800.

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Answer:

7

Step-by-step explanation:

1, 1, 2, 4, 7, 8, 10, 15, 20

median = 7

Due to its subject-specific classification, ink color in pens is a qualitative variable.

Consequently, option (C) is the appropriate choice.

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Answer:

see explanation

Step-by-step explanation:

- 3 | 5x + 6 | + 1 ≥ 6

First step : subtract 1 from both sides

- 3 | 5x + 6 | ≥ 5

Answer:

Vertex - (2, -1)

Axis of Symmetry - x = 2

X intercept - (3,0) (1, 0)

Y intercept (0, 3)

Domain - (negative infinity, positive infinity)

Range - [-1, infinity)

Step-by-step explanation:

I graphed with desmos and found it.

There are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

Given a word of 4 letters of the word "SOLVE".

We are required to find the number of ways the four letters of the word SOLVE if no letter can be used more than once.

Permutation is an arrangement of objects in a definite order of things.

Factorial of a number is the product of it and its lesser numbers upto 1.

Number of letters=4

Number of ways=4!

=4*3*2*1

=24 ways

Hence there are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

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Answer:

abscissa of A = -3

ordinate of B = -6

A+B = -3+(-6)= -3-6=

-9

The value of du becomes 4 by integration.

According to the statement

we have given a two statement which are u - 4x and  u = x + 1.

And we have to find the value of du by the use of integration.

An Integral assigns numbers to functions in a way that describes the data.

So,

From u  - 4x

here du becomes by derivative

du - 4dx/du

du = 4dx/du.  -(1)

And in u = x + 1.

here du becomes

du = dx/du  -(2)

by comparing both terms from equation (1) and (2) we get the value of du

du = 4.

the value of du is 4.

So, The value of du becomes 4 by integration.

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It takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively

A ratio can sometimes be regarded as fraction. While rate has something to do with time.

Given that Jay and Kay can pack the shelves in one aisle of the supermarket in 30 minutes. Kay and Elle take 35 minutes to do the same job. When Jay and Elle work together, the job takes 42 minutes.

Let

The interpretation of the question go thus;

1/J + 1/K = 1/30 ........ (1)

1/K + 1/E = 1/35 .........(2)

1/J + 1/E = 1/42 .........(3)

Make 1/J and 1/E the subject of formula in equation 1 and 2 respectively and substitute them in equation 3

1/J = 1/30 - 1/K  ........ (4)

1/E = 1/35 - 1/K  .........(5)

1/30 - 1/K + 1/35 - 1/K = 1/42

Collect the like terms

- 1/K - 1/K = 1/42 - 1/30 - 1/35

-2/K = (35 - 49 - 42)/1470

-2/K = -56/1470

1/K = 28/1470

Reciprocate both sides

K = 1470/28

K = 52.5 minutes.

Substitute K in both equation 4 and 5

1/J = 1/30 - 28/1470

1/J = (49 - 28)/1470

1/J = 21/1470

Reciprocate both sides

J = 1470/21

J = 70 minutes

1/E = 1/35 - 28/1470

1/E = (42 - 28)/1470

1/E = 14/1470

Reciprocate both sides

E = 1470/14

E = 105 minutes

Therefore, it takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively

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Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, - 5 ) and (x₂, y₂ ) = (- 2, - 9 )

m = [tex]\frac{-9-(-5)}{-2-(-4)}[/tex] = [tex]\frac{-9+5}{-2+4}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

Answer:

In total she got $555 so we have to divide that to see how much she got per hour.

Step-by-step explanation:

y/x=?

$555/15= $37

Now how much money multiplied by how many hours

$37 X 15 = $555

I hope this helps, if you need any more information just comment!

Have an Amazing Day!!!

By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.

In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 120

Reference angle = 60°.

For the coordinates, we have:

sin(-120) = -sin(60) = -1/2.

cos(-120) = -cos(60) = -√3/2.

By applying Pythagorean theorem, we have:

z² = x² + y²

z = √((-1/2)² + (-√3/2)²)

z = √(1/4 + 3/4)

z = √1

z = 1.

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The five-number summary are as follows:

The five-number summary is a set descriptive statistics which consist of the minimum, maximum, median, upper quartile, and lower quartile of a data distribution.

Therefore,

Given:

58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87

Therefore,

Minimum = 58

Lower quartile(Q₁) = 67

Median = 79 + 79 / 2 = 79

Upper quartile(Q₃) = 82

Maximum = 87

Interquartile range = Q₃ - Q₁ = 82 - 67 = 15

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