Come on now, check your book on the "product to sum" identities
![\bf cos({{ \alpha}})sin({{ \beta}})=\cfrac{1}{2}[sin({{ \alpha}}+{{ \beta}})\quad -\quad sin({{ \alpha}}-{{ \beta}})]](https://tex.z-dn.net/?f=%5Cbf%20cos%28%7B%7B%20%5Calpha%7D%7D%29sin%28%7B%7B%20%5Cbeta%7D%7D%29%3D%5Ccfrac%7B1%7D%7B2%7D%5Bsin%28%7B%7B%20%5Calpha%7D%7D%2B%7B%7B%20%5Cbeta%7D%7D%29%5Cquad%20-%5Cquad%20sin%28%7B%7B%20%5Calpha%7D%7D-%7B%7B%20%5Cbeta%7D%7D%29%5D)
Answer:
<em>The distance from Bayfield County to Dodge County is 974 miles.</em>
Step-by-step explanation:
Definition of equidistant: equal distance.
Bayfield Marathon Dodge
+---------------------------------------------+---------------------------------------------+
487 miles 487 miles
The three centers of the counties lie along a straight line. Since Marathon County is equidistant from Bayfield County and Dodge County, then Marathon County is exactly at the midpoint of the segment from Bayfield County to Dodge County. The distances from Bayfield County to Dodge County and from Marathon County to Dodge County are equal. The distance from Bayfield County to Dodge County is
distance = 487 miles + 487 miles = 974 miles
Hi there!
Let's solve this equation step by step!
First add 7 to both sides.
Next we need to take a look at the meaning of the stripes between our variable. Those stripes mean we are dealing with an absolute value function. The absolute value stripes make everything between the stripes positive; also when we plug in a number. In this particular question we can plug in both -13 and 13 at the position of n, because when -13 is made positive, it fulfils the equation.
Hence,
or
~ Hope this helps you!
Lily made $75.36 more than Layla did. If Layla raised her price to $1.00, she would still not make more money than Lily.
Use a proportion to find the number of cupcakes Lily makes in 8 hours. She bakes 7 cupcakes in 10 minutes; we want to know how many she makes in 8(60)=480 (since there are 8 hours and each hour is 60 minutes):
7/10 = x/480
Cross multiply:
7*480 = 10*x
3360 = 10x
Divide both sides by 10:
3360/10 = 10x/10
336 = x
Lily bakes 336 cupcakes.
She sells 2/3 of these; 2/3(336) = 2/3(336/1) = 672/3 = 224 cupcakes sold.
Each cupcake is sold for $1.29; 224(1.29) = 288.96
To find the number of cupcakes Layla makes in 8 hours, we set up a different proportion. We know she bakes 8 cupcakes in 12 minutes; we want to know how many she bakes in 8(60) = 480 minutes:
8/12 = x/480
8*480 = 12*x
3840 = 12x
Divide both sides by 12:
3840/12 = 12x/12
320 = x
She bakes 320 cupcakes. She sells 75% of those; 75% = 75/100 = 0.75:
0.75(320) = 240
Each of those 240 cupcakes sells for $0.89:
0.89(240) = 213.60
This means Lily makes 288.96-213.60 = 75.36 more than Layla.
If Layla raised her price to $1.00, she would make 1(240) = $240; this is still less than Lily.
Answer:
4+√55= 11.42
4-√55= -3.42
Step-by-step explanation:
- w² − 8w − 39 = 0
- w²- 2*4w + 16- 55=0
- (w-4)²=55
- w-4=√55 ⇒ w= 4+√55= 11.42
- w-4=- √55 ⇒ w= 4-√55= -3.42
