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3 years ago

10

Find c to two decimal places and find the measure of angle B. Angle A = 58°, Side AC = 5, Side BC = 8, Find side C. Angle C is 9

0°.

1 answer:

KATRIN_1 [288]3 years ago

5 0

Answer:

c = 9.43
m∠B = 32°

Step-by-step explanation:

Side c = AB can be found using the Pythagorean theorem:

c² = a² + b² = 8² +5² = 89

c = √89 ≈ 9.43

__

Angle B is the complement of angle A, so is ...

B = 90° -A = 90° -58° = 32°

c is approximately 9.43; the measure of angle B is 32°.

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black pencils cost 75 naira each and colour pencils cost 105 naira each if 24 mixed pencils cost 2010 naira how many of them wer

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Answer:

number of black pencils is 17

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3 years ago

In XYZ, mX=90 and mY=30.In TUV,mU= 30 and mV=60. Which is true about the two triangles? XYZ=TUV, XYZ= VUT,No congruency statemen

Flauer [41]

Answer:

No congruency statement can be made because the side length are unknown.

Step-by-step explanation:

The sum of the measures of all interior angles in a triangle is always 180°.

In triangle XYZ,

$m\angle X=90^{\circ}\\ \\m\angle Y=30^{\circ},$

then

$m\angle X+m\angle Y+m\angle Z=180^{\circ}\Rightarrow m\angle Z=180^{\circ}-90^{\circ}-30^{\circ}=60^{\circ}$

In triangle TUV,

$m\angle U=30^{\circ}\\\\m\angle V=60^{\circ},$

then

$m\angle T+m\angle U+m\angle V=180^{\circ}\Rightarrow m\angle T=180^{\circ}-30^{\circ}-60^{\circ}=90^{\circ}$

We have two triangles with congruent angles but we have no information about side lengths. Therefore, can not be made because the side length are unknown. Correct option is last option.

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3 years ago

Read 2 more answers

$150 for repair, $50 per week after repair to operate. X=#of weeks and y=total cost. Equate using slope-intercept form

Cloud [144]

Answer:

y=150+50x

Step-by-step explanation:

Given data

Repair= $150

weekly charge = $50

X=#of weeks and y=total cost.

Hence the expression in slope-intercept form is

y=150+50x

8 0

3 years ago

Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ti

spayn [35]

Answer:

(a) $D(x)=-2,500x+60,000$

(b) $R(x)=60,000x-2500x^2$

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

$\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500$

Therefore, we have:

$y=-2500x+b$

At point (12,30000)

$30000=-2500(12)+b\\b=30000+30000\\b=60000$

Therefore:

$D(x)=-2,500x+60,000$

(b)Revenue

$R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2$

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

$R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12$

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

$R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0$

Therefore:

Optimal ticket price:$12
Maximum Revenue:$360,000

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3 years ago

Suzanne is looking at taking out a personal loan. Opportunity Loans is offering her $1600 at 3.45% for 1 year, with interest com

AleksAgata [21]

Step-by-step explanation:

So the general formula for compound interest is $A = P(1+\frac{r}{n})^{nt}$ where r is the interest rate, t is the time in years, and n is the amount of compounds per year. So plugging in the values for both equations you'll get

Opportunity Loans:

$A = 1600(1+\frac{0.0345}{12})^{(12)(1)}$

$A = 1600(1.002875)^{12}$

$A \approx 1600(1.035)$

$A = \$1,656.08$

Now to find the interest accrued on this loan you simply subtract 1600 from the A or final amount

$Interest=1656.08-1600\\Interest=56.08$

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$A = 1600(1+\frac{0.042}{4})^{(4)(1)}$

$A = 1600(1.0105)^4$

$A \approx 1600(1.042)$

$A = 1,668.27$

To find the interest we do the same thing we did in the previous problem

$interest = 1668.27-1600\\interest=68.27$

Opportunity loans has the least amount of interest after a year

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2 years ago