The intersection of three lines at one point and the measures of three angles are shown in this figure.

Given:

The graph of a triangle ABC.

A line is parallel to AC and passes through the point D.

To find:

The point at which the intersection of this parallel line be with the line BC.

Solution:

From the given figure it is clear that A(1,7), B(9,7), C(9,1) and D(5,7).

Slope of AC is

[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]Slope=\dfrac{1-7}{9-1}[/tex]

[tex]Slope=\dfrac{-6}{8}[/tex]

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

Slope of parallel lines are same. So, the slope of parallel line is also [tex]-\dfrac{3}{4}[/tex].

The parallel line passes through D(5,7) with slope [tex]-\dfrac{3}{4}[/tex]. So, the equation of the line is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-7=-\dfrac{3}{4}(x-5)[/tex]

[tex]y=-\dfrac{3}{4}(x)+\dfrac{15}{4}+7[/tex]

[tex]y=-\dfrac{3}{4}(x)+\dfrac{28+15}{4}[/tex]

[tex]y=-\dfrac{3}{4}(x)+\dfrac{43}{4}[/tex]              ...(i)

From the given graph it is clear that the line BC is a vertical line. So, the x-coordinates of all the points lie on BC are the same, i.e., 9.

Putting x=9, we get

[tex]y=-\dfrac{3}{4}(9)+\dfrac{43}{4}[/tex]

[tex]y=\dfrac{-27}{4}+\dfrac{43}{4}[/tex]

[tex]y=\dfrac{16}{4}[/tex]

[tex]y=4[/tex]

Therefore, the point at which the intersection of this parallel line be with the line BC is (9,4).

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:

34.65

Step-by-step explanation:

495x0.07=34.65

Answer:

x+8y= -5

Step-by-step explanation:

1) the required equation of the line has an slope-interception form:

y=mx+i, where m - slope, i - interception.

2) if the given point belongs to the required line, then it is possible to substitute its coordinates into the equation, then:

0=m*(-5)+i; ⇔-5m+i=0;

3) if the slope m= -1/8, then

-5*(-1/8)+i=0, ⇒5/8+i=0; ⇒ i= -5/8.

4) finally, the required equation is (m= -1/8; i= -5/8):

y= (-1/8)*x-5/8; ⇔ x+8y= -5.

note: the suggested solution is not the only way.

Answer:

They made 2 batches

Step-by-step explanation:

If the factory used ⅔, and 1 batch is ⅓, the factory made 1 batch for each 3rd they used. ⅔, 2 batches

Answer:

x > -13

Step-by-step explanation:

Let x be the number

2x+8 > -18

Subtract 8 from each side

2x+8-8 > -18-8

2x> -26

Divide each side by 2

2x/2 > -26/2

x > -13

Answer:

x > -13

Step-by-step explanation:

Let x be the number

2x+8 > -18

Subtract 8 from each side

2x+8-8 > -18-8

2x> -26

Divide each side by 2

2x/2 > -26/2

x > -13

Answer:

2z + 5

Step-by-step explanation:

you have to combine like terms

subtract 4z - 2z and you get 2z

the number with the variable next to it goes first not the constant

2z + 5

the variable is z and the constant is 5 because it doesn't have variable next to it

hope this makes sense and helps :)

tell me if you have any questions

Step-by-step explanation:

Here as the like terms only are 4z and -2z so,

We simplify the like terms:

5 + 4z - 2z. [B.O.D.M.A.S rule] (subtraction only)

= 5 + 2z (Ans)

Answer:

1.921

Step-by-step explanation:

Answer:

123 km/h

Step-by-step explanation:

the formula for the unit rate would be 82/40

82 divided by 40 is 2.05km/m

Then you have to convert 2.05 km/m to km/h

multiply 2.05 times 60 and your answer is 123 km/h

Answer: 123 km/h

Step-by-step explanation:

Answer:

ᴀ.)

Step-by-step explanation:

Hope you get it right!! :)

Answer:

The answer is 1/10

Step-by-step explanation:

Answer:

y = (1/4) 2^x

Step-by-step explanation:

Remark

y = a * x^n is the general equation. Let's see what that means.

Solution

Solve for x

t_12 = a x^12

1024 = a x^12

t_8 = a x^8

64 = a x^8

Now divide the two equations.

1024/64 = a x^12/a x^8       Cancel out the as

1024 / 64 = x^12 / x^8

16 = x^(12 - 8)

16 = x^4                               Take the 4th root of both sides.

[tex]\sqrt[4]{x^4}[/tex]  =  [tex]\sqrt[4]{16}[/tex]

x = 2

Go back and solve for a

y_12 = a x^12

1024 = a 2^12

1024 = a 4096                   Divide by 4096

1024 / 4096 = a

a = 1/4

Problem 7

a) First of negative numbers are probably not a good idea. It means that the population is going to decrease. That's not what will happen if you take care of the fruit flies.

So for the domain, 0 is a good starting point.

That will give you 100 flies on day 0. That's how many you bought.

I'm not a biologist so I have no idea in the world how long a fruit fly will live even with the best of care. I'm going to try 60 days and see what happens.

y = 100 * 1.05 ^60

y = 100 * 18.68

y = 1868

Is this number reasonable? Even with the biggest olive jar you can find, and the best care, I don't think that number is realistic. It's too large. Eventually all will die of disease because they are living in their own waste. So Let's try 20 days

y = 100 * 1.05^20

y = 100 * 2.65

y = 265

That's a lot more reasonable. So for convenience sake let us say that 265 flies could live for 20 days

So to answer the question

The domain would be 0 to 20

The range would be 100 to 265

b)

2 weeks = 2*7 days

2 weeks = 14 days

y = 100 * 1.05^14

y = 100 * 1.98

y = 198 fruit flies.

Answer:

16.65

Step-by-step explanation:

15 percent of 111 is the same as 15 per hundred of 111. We can therefore make the following equation:

15/100 = X/111

To solve the equation above for X, you first switch the sides to get the X on the left side, then you multiply each side by 111, and then finally divide the numerator by the denominator on the right side to get the answer. Here is the work to illustrate:

15/100 = X/111

X/111 = 15/100

X*111/111 = 15*111/100

X = 1665/100

X = 16.65

or

The work above shows the long way to explain how to calculate 15 percent of 111 in order to give you a foundation and better understanding of how to calculate percentage. In the future, you could use this simplified formula:

(Y * P)/100

In our problem "What is 15 percent of 111?", Y is 111 and P is 15:

(111 * 15)/100 = 16.65

And once again you see that the answer is 16.65.

Answer:

740

Step-by-step explanation:

If we substitute "what number" in the question "111 is 15 percent of what number?" with 740, we get this sentence: 111 is 15 percent of 740. Since this statement is true, we know that our answer is correct.

Following shows the steps on how to derive this formula

Step 1: If 15% of a number is 111, then what is 100% of that number? Setup the equation.

111          Y

------  =   -------

15         100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

15Y = 111 x 100

15Y = 11100

Y = 11100

100 = 740

Formula = Number x 100     111 x 100

                 --------------------- = ------------  = 740

                   Percent              15

Hope this helps

Answer:

big

Step-by-step explanation:

pp

Answer:

4536

Step-by-step explanation:

Hesap makinesi kulan

Answer:

552 eggs

Step-by-step explanation:

A dozen is equal to 12

Solve:

Multiply 46 by 12

Answer:

125 cubic cm

Step-by-step explanation:

Length^2 = 25 so each side length is 5cm

5^3 = 125 cubic cm

Answer:

D. 4.15c + .94s

Step-by-step explanation:

4.15 is how much the cashews cost per pound, this multiplied by c would be the full cost of however many pounds of cashews are being purchased.

.94 is how much the sugar costs per pound, this multiplied by s would be the full cost of however many pounds of sugar is being purchased.

to get the full cost of both, you add these equations together (4.15c + .94s)

Answer:

(A) Population data

(B) The figures

(C) The classification of votes by political party

Step-by-step explanation:

(A) These results summarize population data. The population is the total 3,889 voters from whom information was collected.

The samples would be

- Voters registered as Democrats  (1,633)

- Voters registered as Republicans  (1,206)

- Independent Voters  (1,050)

The total of members in each sample equals the total number of people in the population.

(B) A descriptive aspect of the result is the figures or percentages. They describe how (in percentage) voters penned their votes for Brown and how they penned their votes for Whitman. NOTE: To get the percentage or fraction of those who voted for Whitman, simply subtract the percentage of Brown's supporters from a total of 100%.

(C) An inferential aspect of the results is the classification of votes by different parties (the samples are the different parties involved here). This helps to infer the sources of support for Brown and the sources of support for Whitman.

For example, if the total votes for Brown (in population result analysis) are low, the Republicans are the major reason why!

Answer:

cool how much he got

Step-by-step explanation:

Answer:

3-9= the number of people who at chicken wings and the number of people who ate chicken wings were 2. By the way i dont know if did my math absolutley correct. sry:(

Answer:

See the attached document

Answer:

Step-by-step explanation:

For this question, it's C

Answer:

3/2x²+28x+130

Step-by-step explanation:

Area of shaded region = Area of rectangle – Area of triangle

Area of rectangle:

[tex](2x + 15)(x + 10) = \\2x {}^{2} + 35x + 150[/tex]

Area of triangle:

[tex] \frac{1}{2 } \times (x + 4)(x + 10) = \\ \frac{1}{2} x {}^{2} + 7x + 20[/tex]

then subtract

Answer:

75.36 inches

Step-by-step explanation:

C = π·d

C = 3.14(24)

C = 75.36

Answer:

The final balance is $5,796.37.

The total compound interest is $796.37.

Step-by-step explanation:

Answer:

2

2

3x

Step-by-step explanation:

1.) we can divide both sides by three to get

(3x+6)/3=x+?

x+2= x+?

from here we can tell that ?=2

2.) Let's start by dividing both sides by negative one

(x-2)/ -1= ?-x

simplify

-x+2= ?-x

Here we get ?= 2

3.)

Let's mulitply both sides by 5 to get

15x-10= 5(?-2)

15x-10 = 5?-10

15x= 5?

3x= ?

the answer here is 3x

Answer:

1 if u cut  all of them in half

Step-by-step explanation: