The value of x is 67°
<u>Step-by-step explanation:</u>
Given that
PN=LN
NP||MQ
QL bisects <PQM
therefore <PQL=<LQM
NP||MQ and NM is a transversal
<PNL+<LMQ=180°(angles on the same side of the transversal are supplementary)
<PNL+54=180°
<PNL=180-54=126°
Consider ΔPNL
since PN=NL,the triangle is isocelus
<NPL=<NLP=a
<NPL+<NLP+<PNL=180°
a+a+126=180°
2a+126=180
2a=180-126
=54°
a=54/2=27°
consider the point L
<NLP+<PLQ+<MLQ=180°
27+70+<MLQ=180
<MLQ=180-97=83°
consider ΔLQM
<LQM+<LMQ+LMQ=180
<LQM+83+54=180
<LQM=180-(83+54)=180-137=43°
<PQL=43°(since<PQL=<LQM)
considerΔPQL
x+70+<PQL=180°
x+70+43=180°
x+113=180
x=180-113
=67°
The value of x is 67°
Answer:
See Explanation
Step-by-step explanation:
<em>The question is incomplete; So, I will solve generally</em>
Required
Quotient of two terms where 1 has a coefficient of 8
The quotient (Q) of a and b can be represented as:

Where a and b are the terms
For a or b to have a coefficient of 8, then a or b must be

Where x is the variable
So, the quotient can be expressed as any of:



<em>As long as one of the terms has a coefficient of 8</em>
Answer:
The number of sweatshirts to sell in order to break even is 40
Step-by-step explanation:
Let x be the number of sweatshirts. We are looking for break even, which means profit is 0 here.
And softball team purchased a box for 240$ and for printing it costs 12$ per shirt.
So total cost of sweatshirts = 240+12x
And selling price is 18$ per shirt.
Hence selling price for x shirts = 18x.
Now we need to graph y=18x and y=240+12x first and then look for intersection to find the break even.
From the graph attached, we can see that both lines are intersecting at x=40.
Hence number of sweatshirts to sell in order to break even is 40.
Answer:

Step-by-step explanation:
The blue parabola is only a translated version of the red parabola. The standard form of a vertical parabola centered at (h,k), that is, a parabola whose axis of symmetry is parallel to y-axis, is of the form:

Where:
,
- Horizontal and vertical components of the vertex with respect to origin, dimensionless.
- Vertex constant, dimensionless. (If C > 0, then vertex is an absolute minimum, but if C < 0, then vertex is an absolute maximum).
Since both parabolas have absolute minima and it is told that have the same shape, the vertex constant of the blue parabola is:

After a quick glance, the location of the vertex of the blue parabola with respect to the origin is:

The standard form of the blue parabola is
. Its expanded form is obtained after expanding the algebraic expression and clearing the independent variable (y):


Then, the blue parabola is represented by the following equations:

c ≈ 16.7 ( to 1 dec. place ) → d
since triangle ABC is right use the cosine ratio to find c
cos33° =
= 
multiply both sides by c
c × cos33° = 14 ( divide both sides by cos33° )
x =
≈ 16.7 ( to 1 dec. place )