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2 years ago

What is the length of AC ? 3ft 4ft 9ft 18ft

Mathematics

1 answer:

WINSTONCH [101]2 years ago

5 0

ΔACB and ΔMNB are similar. Therefore the corresponding sides are in proportion:

$\dfrac{AC}{MN}=\dfrac{CB}{NB}\\\\MN=9\ ft\\CB=2\cdot3\ ft=6\ ft\\NB=3\ ft$

Substitute:

$\dfrac{AC}{9}=\dfrac{6}{3}\\\\\dfrac{AC}{9}=2\ \ \ \ |\cdot9\\\\AC=18\ ft$

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Marla did 65 sit ups each day for one week.Use the distributive property to show an expression you can use to find the total num

poizon [28]

The distributive property <span> lets you multiply a sum by multiplying each addend separately first and then summing the products together.
Marla did 65 x 7 = 455 sit-ups during the week

65 sit-ups can be written as 60+5 sit ups or as 50+15 sit-ups or as 40+25 sit-ups (these are just examples)

Applying the distributive property:
Marla did: (60 x 7) + (5 x 7) = 455 sit-ups during the week, or
Marla did: (50 x 7) + (15 x 7) = 455 sit-ups during the week, or
Marla did: (40 x 7) + (25 x 7) = 455 sit-ups per week

You can try this with any two numbers whose sum is 65 and all will give you the same answer.

</span>

7 0

2 years ago

The graph represents the speed at which Pete’s marble travels.

AfilCa [17]

Answer:

Step-by-step explanation:

Here, we simply want to know who will reach the 6-foot mark sooner

Mathematically, we need to get the slope from the graph

Looking at the graph, we can see that the 3 ft mark was reached at exactly 2 seconds

So what this mean is that, in 4 seconds, the 6 ft mark will be reached

This makes up the fact that the speed for Pete’s travel is 1.5 ft/ secs

Now compare this with what Stephano has, which is 2.25 ft/ s

we can see that stephano is traveling at a better speed and will reach the 6 ft mark first

So the correct option is B

5 0

2 years ago

I ate twice as many apples as bananas and 3 times as many blueberries as bananas. If I ate 12 fruits and berries altogether, how

igor_vitrenko [27]

2 bananas 4 apple and 6 blueberries

8 0

2 years ago

Q: Angelica uses the point (4,3) to represent the location of her house and uses the point (10,8) to represent the location of a

oksian1 [2.3K]

Answer:

The answer to your question is 7.8 mi

Step-by-step explanation:

Data

H (4,3)

G (10, 8)

Process

1.- Use the distance between to points formula to find the distance

dHG = $\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}$

x1 = 4 y1 = 3

x2 = 10 y2 = 8

2.- Substitution

dHG = $\sqrt{(10 - 4)^{2} + (8 - 3)^{2}}$

3.- Simplification

dHG = $\sqrt{6^{2} + 5^{2}}$

dHG = $\sqrt{36 + 25}$

dHG = $\sqrt{61}$

4.- Result

dHG = 7.8 mi

4 0

2 years ago

Read 2 more answers

Two airplanes are flying to the same airport. Their positions are shown in the graph. Write a system of linear equations that re

Liono4ka [1.6K]

To write the system we need the slope of each line and at least one point on the line. The two lines to consider will be the lines connecting the location of each plane to the airport they are flying to. It is also worth noting that the coordinates of the airport represent the point of intersection of the two lines and thus the solution to the system.

1. slope of the line connecting airplane one and the airport: m = 2 you can see this clearly if you graph the two points. From airplane 1 location we rise 8 units and move to the right 4 units to get to the airport. Slope is defined as rise over run: so 8 divided by 4 = 2(the slope) Now substitute the slope and the point (2,4) into point-slope form of a line:

y - 4 = 2(x -4) the standard form of this equation is 2x - y = 0

2. slope of the line connecting airplane 2 and the airport: m = - $\frac{1}{3}$ To find this slope, simply observe the vertical change of down 3 and a horizontal shift of right 9 from the airport to airplane 2. Now substitute this slope and and the point (15,9) into point-slope form of a line:

y - 9 = $- \frac{1}{3}$ (x - 15) the standard form of this equation is:
x + 3y = 42

Let's write the system:
2x - y = 0
x + 3y = 42
Multiply the first equation by 3 to get the new system
6x - 3y = 0
x + 3y = 42 add these two equations to get an equation in terms of x

7x = 42 thus x = 6 and substituting this value into 2x - y = 0 we see y = 12
In other words, we have proven that the location of the airport is in fact the solution to our system.

PS: You just have to do a little algebra to get from point-slope form of the two equations to standard form. I did not show this process, but if you need it just let me know... thanks

6 0

2 years ago