a grocery store sells a bag of 4 lemons for $0.79. Which pricing option would result in the same unit price for each lemon

In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$ [asy] unitsize(2 cm); pair D, E,

sergey [27]

Answer:

Step-by-step explanation:

The answer to this question is 12+6sqrt3.

This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.

The square root of 108 simplified=6sqrt3.

Then you add them together and get 12+6sqrt3.

5 0

2 years ago

I set a goal to drink 64 ounces of water day.If i drink 10 1/3 ounces in the morning,15 1/2 ounces at noon,and 20 5/6 at dinner

Vedmedyk [2.9K]

First find how much you've had. Make the fractions with similar denominaters: 1/3(2)=2/6, 1/2(3)=3/6, 5/6(1)=5/6. Now add the fractions: 2/6+3/6+5/6=10/6 or 1 4/6 or 1 2/3. Then add the whole numbers: 10+15+20+1=46. So you've had 46 2/3 oz now subtract that from how much you need: 64-46 2/3= 63 3/3-46 2/3=17 1/3. You still need 17 1/3 water :)

6 0

1 year ago

Given that tangent theta = negative 1, what is the value of secant theta, for StartFraction 3 pi Over 2 EndFraction less-than th

Rashid [163]

Answer:

$sec(\theta)=\frac{2}{\sqrt{2} }=\sqrt{2}$

Step-by-step explanation:

Start by noticing that the angle $\theta$ is on the 4th quadrant (between $\frac{3\pi}{2}$ and $2\pi$ . Recall then that in this quadrant the functions tangent and cosine are positive, while the function sine is negative in value. This is important to remember given the fact that tangent of an angle is defined as the quotient of the sine function at that angle divided by the cosine of the same angle:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

Now, let's use the information that the tangent of the angle in question equals "-1", and understand what that angle could be:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\-1=\frac{sin(\theta)}{cos(\theta)}\\-cos(\theta)=sin(\theta)$

The particular special angle that satisfies this (the magnitude of sine and cosine the same) in the 4th quadrant, is the angle $\frac{7\pi}{4}$

which renders for the cosine function the value $\frac{\sqrt{2} }{2}$ .

Now, since we are asked to find the value of the secant of this angle, we need to remember the expression for the secant function in terms of other trig functions: $sec(\theta)=\frac{1}{cos(\theta)}$

Therefore the value of the secant of this angle would be the reciprocal of the cosine of the angle, that is: $sec(\theta)=\frac{2}{\sqrt{2} }=\sqrt{2}$

6 0

1 year ago

Read 2 more answers

How do I factorise 35x+55

densk [106]

Find what is common between 35 and 55....and that would be 5....so factor 5 out

35x + 55 =
5(7x + 11) <==

5 0

2 years ago

Read 2 more answers

When choosing a new school mascot, 80 students voted for an eagle, and 160 students voted for a bulldog. Rounded to the nearest

makvit [3.9K]

Simple.
100% of the student body is 160 + 80, which is 240.

160 is 66.7% of 240.
So 66.7% voted for a bulldog.

Hope this helps!