State whether the given measurements determine zero, one, or two triangles. b = 84°, b = 28, c = 25

Answers

Answer 1

if B= 84°, b=28 and c= 25
Using the cosine formula:
SinB/b = SinC/c
Sin84°/28 = SinC/25
SinC = (Sin84°)(28)/25
C = 62.6° 0r 117.4°
When B = 84°, it is not possible for C = 117.4°
so, angles of triangles did not exceed 180°
it means there is only one triangle

Related Questions

1/2(6x-4)=2/3x How do i solve this?

Answers

Apply distributive property.

3x-2=2/3x

Multiply all terms by 3 so we won't have to deal with fractions.

9x-6=2x

Subtract 9x from both sides

-6=-7x

Divide both sides by -7

x= 6/7

Final answer: x=6/7

A triangle has measurements of 39, 52, and 65 units. Is it a right triangle?

Yes
No
Not enough information to tell

Answers

Hi!

We can use the Pythagorean Theorem to see if it is a right triangle.

The Pythagorean Theorem is a² + b² = c².

c = the longest side, or the hypotenuse. In this case, the hypotenuse should be 65.
39 can be a, and 52 could be b, or 52 could be a, and 39 could be b. It doesn't matter.

39² + 52² = 65²

Is this equation true?

Yes! This equation is true.

The answer is Yes, this is a right triangle.

Hope this helps! :)

yes it is an right triangle hoped it helps !!!!!!

a 23 gram sample of a substance thats a by-product of fireworks has a K-value of .13. whats the substances half life in days

Answers

Given:
Initial mass, m₀ = 23 g
Decay constant, k = 0.13

Exponential decay obeys the equation
[tex]m(t)=m_{0} e^{-kt}[/tex]
where t = time, days

For half life, the mass is m = m₀/2.
Therefore
[tex]e^{-0.13t} = \frac{1}{2} \\ -0.13t = ln(0.5)\\t= \frac{ln(0.5)}{-0.13} =5.33[/tex]

Answer: The half life is 5.33 days

Answer:

5.3 is the right answer.

Step-by-step explanation:

The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.

Part A: Determine the vertex. What does this calculation mean in the context of the problem?

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Answers

f(x) = -x^2 + 20x - 75 = (x-5)*(-x + 15)
The two x-intercepts are x = 5 and x = 15, which are the two values of x where f(x) = 0. The vertex is located halfway between these two points, so where x = 10. When x = 10, f(x) = 25, so the vertex of this graph is (10, 25).

Part A: The vertex is (10, 25). The vertex represents the point where the profit is a maximum. When 10 photos are printed, the profit is $25.

Part B: The two x-intercepts are x = 5 and x = 15. This shows where the profit is $0. When 5 photos or 15 photos are printed, the profit is $0.

Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula V=4/3 pi r^2

Answers

It is r^3 in the volume formula.

V=(4πr^3)/3 multiply both sides by 3

3V=4πr^3 divide both sides by 4π

r^3=3V/(4π) take the cube root of both sides

r=((3V)/(4π))^(1/3)

The amount of an ordinary $7,500.00 annuity for 3 years at 12 percent compounded quarterly is

Answers

[tex]\bf \qquad \qquad \textit{Future Value of an ordinary annuity}\\ \left. \qquad \qquad \right.(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right][/tex]

[tex]\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &7500\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4\\ t=years\to &3 \end{cases} \\\\\\ A=7500\left[ \cfrac{\left( 1+\frac{0.12}{4} \right)^{4\cdot 3}-1}{\frac{0.12}{4}} \right][/tex]

Answer:

$180,997.50.

Step-by-step explanation:

1. On TABLE 14-1 Future Value of $1.00 Ordinary Annuity, select the periods row corresponding to the number of interest periods.

2. Select the rate-per-period column corresponding to the period interest rate.

3. Locate the value in the cell where the periods row intersects the rate-per-period column.

4. Multiply the annuity payment by the table value from step 3.

Future value = annuity payment × table value

FV = $7500.00 * 24.133 = $180,997.50

Find the surface area of each figure to the nearest tenth. Show your work, please

Answers

Pyramid surface area (total): Lateral surface area + Base area

Lateral surface area = [tex] \frac{2p*a}{2} [/tex] where p is the base perimeter and a the apothem.

The base is a sqaure so, find the area of the square.

Base Area = 16*16 = 256 in²

Calculate the perimeter = 16*4 = 64 in

LSA = (64*17)/2 = (64*17)/2 = 1088/2 = 544 in²

TSA = 544+256 = 800 in²

Total surface of cone: LSA + Base Area

LSA = πra

Let's find the apotheme. Apply Pitagora, again the hypothenuse is the apotheme. The legs are the radius and the height.

a = √8²+3² = √64+9 = √73 ≈ 8,5 in.

Base area (area of the circle) = πr² = 3²*π = 9π in²

LSA = 3*8,5*π = 25,5π in²

TSA = 25,5π+9π = 34,5π = 34,5*3,14 = 108,3 in²

how many solutions does this system have -3x+6y=10 -3x+6y= -4

Answers

0 because if u subtract the equations you get 0x + 0y = 14 which is not possible

-3x+6y=-4
-3x+6y=10

0x+0y=14

Find the product of (2x + 5y)2.

Answers

4x +10y is the product of (2x+5y)2

Distribute 2 to 2x and 5y using PEMDAS to get 4x+10y

A quadratic equation is shown below:

25x2 + 10x + 1 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answers

hello :

help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions

HELP!!!!
Use the following data set and a separate piece of paper to make a line plot that will help you to answer questions 2-7.
(6, 4, 4, 5, 1, 8, 10, 7, 8, 6, 6, 7, 5, 4, 6)
Add a box and whisker plot to the graph. Clearly mark the ends of box by drawing vertical lines and labeling their values on the horizontal axis. What are the ends of the box and whisker plot?

A. 1 and 6

B. 4 and 7

C. 4 and 8

D. 5 and 7

Answers

1,4,4,4,5,5,6,6,6,6,7,7,8,8,10

minimum = 1
Q1 = 4
Q2 (median) = 6
Q3 = 7
maximum = 10

The beginning and end of the " box " are Q1 and Q3.....4 and 7

What is the length of diagonal ac in parallelogram ABCD if the diagonal BD = 10cm which is twice the diagonal AC?

Answers

Final answer:

The length of the diagonal AC in parallelogram ABCD is 5 cm.

Explanation:

Given that the diagonal BD is twice the length of diagonal AC, we can represent the length of diagonal AC as x. So, the length of diagonal BD would be 2x. From the given information, we know that BD = 10 cm. Therefore, we can write the equation 2x = 10 to solve for x. Dividing both sides of the equation by 2 gives x = 5. So, the length of diagonal AC is 5 cm.

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Final answer:

In the given parallelogram, the length of the diagonal AC is 5 cm, given that the length of the diagonal BD is twice that of AC.

Explanation:

The question pertains to the properties of a parallelogram. In this case, it has been provided that diagonal BD (10 cm) is twice the length of the other diagonal AC. This implies that the length of diagonal AC is half the length of BD. Therefore, to find the length of AC, take the length of BD and divide by 2:

AC = BD / 2 = 10 cm / 2 = 5 cm

So, the length of diagonal AC is 5 cm.

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Which has a greater area, a square with sides that are x - 1 units long or a rectangle with a length of x units and a width of x - 2 units?

Answers

Area of square = a^2...where a is the length of 1 side
A = (x - 1)^2
A = (x - 1)(x - 1)
A = x^2 - 2x + 1

Area of rectangle = L * W
A = x(x - 2) = x^2 - 2x

The greater area would be the square <==

at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 when gas cost $2.20 per gallon on average

Answers

The average cost represents the slope of the line of the graph.
Increasing the slope of the graph increases the steepness of the line.
Therefore, increasing the average cost of gas from $1.50 to $2.20 will increases the steepness of the line. (i.e. the line becomes closer to the vertical line).

Solve the following equation by transforming it into a perfect square trinomial. x2 – 4x = 5 will mark as brilliant

Answers

x^2 - 4x = 5
(x - 2)^2 - 4 = 5
(x - 2)^2 = 9

x- 2 = +/- sqrt9 = +/- 3
x = 3 + 2 or -3 + 2
solution set is {-1 , 5}

The solution of the given equation is -1 or 5

What is an equation?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given is an equation, x²-4x = 5,

we need to transform it into a perfect square,

The equation is =

x²-4x = 5

Add 4 to each side,

x²-4x+4 = 5+4

x²-4x+4 = 9

(x-2)² = 9

Solving for x,

x-2 = √9

x-2 = ±3

x = -1 or x = 5

Hence, the solution of the given equation is -1 or 5

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If y varies directly with x and y = 10 when k = 10, what is the value of x?

Answers

y = k *x
y=10 ; k=10

10 = 10*x
x = 10/10 = 1

x =1

Table to estimate how many pounds of dog food his dog eat in one year which of the following would be the best strategy

Answers

Let's say that the dogs eat 50 lbs of food in 50 days. That would mean they eat 50/50 = 1 pound per day. Notice I divided the weight over the number of days. The dog eats 1 pound per day, for 365 days, so in total it eats 365*1 = 365 pounds. This is just a hypothetical example.

In general, if x is the number of days to eat 50 pounds of food, then x/50 is the expression representing the amount eaten per day (in pounds). Finally 365*(x/50) is the expression representing the total amount eaten over the whole year.

This is why the final answer is choice C

Find the sum of the geometric sequence. (1 point) 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen

Answers

GP = 1/2 , 1/4 , 1/8 , 1/16
1st) the common ratio is (1/4 : 1/2 ) = 1/2, so r =1/2
2nd) the sum of a GP is:

S= a(1-rⁿ)/(1-r)

S=(1/2).[1-(1/2)⁴]/(1-1/2) = 15/16

Answer:

31/16

Step-by-step explanation:

Half of the population of cool town owns a bicycle, and 25% of the population owns a car. if 10% of the population owns both a car and a bicycle, what is the probability that a person chosen at random from cool town owns either a car or a bicycle or both?

Answers

75%...................

HELP PLEASE! Which of these shows the following expression factored completely? 6x^2-13x=5

a (3x-1)(2x+5)
b (3x-5)(2x-1)
c (3x-1)(2x-5)
d (3x-5)(2x+1)

Answers

c (3x+1)(2x-5)
You have to try whatever factoring method you've been taught, but this is the answer.

The solution is: the following expression factored completely,

6x^2-13x=5 is: c (3x-1)(2x-5)

What is an expression?

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Here, we have,

we have,

6x² - 13x = +5

6x² - 13x - 5 = 0

6x² - 15x + 2x - 5 =0

so, we get,

(3x-1)(2x-5) = 0

The sign of the constant term is the product of the signs of the constants in the binomial factors: (+1)·(+5). We want a positive sign for the constant, so both binomial factor constants must have the same sign.

When the signs of the binomial factor constants are the same, the x-term constant will match them. Thus, for a positive x-term constant, both binomial factor constants must be positive.

The signs of the x-term and the constant term are both positive, so the signs of the constants in the binomial factors must be the same and must both be positive. The only offering that meets that requirement is

... C (3x-1)(2x-5)

Hence, The solution is: the following expression factored completely, 6x^2-13x=5 is: c (3x-1)(2x-5)

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Two pools are being filled with water. To start, the first pool contains 2200
liters of water and the second pool contains 1840
liters of water. Water is being added to the first pool at a rate of 21.25
liters per minute. Water is being added to the second pool at a rate of 32.5
liters per minute.
(PLEASE ANSWER QUICK)

Answers

2200 + 21.25X = 1840 +32.50X

subtract 1840 from each side

360+ 21.25X= 32.50X

subtract 21.25x from each side

360=11.25X

x= 360/11.25 = 32 minutes pool will have the same amount

21.25*32 = 680+2200 = 2880 liters

32.5*32 = 1040 + 1840=2880 liters

it will take 32 minutes and they will have 2880 liters each

Ue can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?

Answers

The rate of Sue is 1 car per hour: 1 (c/h)

then the rate of Steve is 2 (c/h) , because Steve works faster, he can wash twice the number of cars, for the same amount of time.

Thus If Steve and Sue work together, they can wash 1 + 2 = 3
(cars per hour).

That is, the rate of Steve and Sue working together, is 3 (c/h).

In the first 30 minutes, Sue washes half of the car.

The remaining half will be washed at a rate of 3 (c/h)

The main formula is Work = Time * Rate

where Work is washing (1/2)c, and rate is 3(c/h)

Time=Work/Rate = [tex] \frac{ \frac{1}{2} c}{3 \frac{c}{h} }= \frac{1}{6}h [/tex]

1/ 6 h =(1/6)*60 min = 10 min

Answer: 10 min

.help me with this please thanks

Answers

i would say B .
They are not like terms because they are not all the same

I need help with all of these

Answers

13. "Colinear" -> "on the same line" -> A,B,E
14. "Coplanar" -> "on the same plane" -> B,C,D,E
15. Planes are name by 3 non-colinear points --> Plane ACE

18. Two points -> G &F
A line -> Line GF
19. Plane T and Plane S

D: region D helppppppppp

Answers

you only hace to change x equal 0 and y equal 0, answer is D

at maximum speed, an airplane travels 1680 miles against the wind in 5 hours. Flying with the wind, the plane can travel the same distance in 4 hours.

Answers

The speed of the airplane with the wind is 420 mph, and against the wind is 336 mph. The speed of the wind is 84 mph.

To find the speed of the wind, we use the following formulas:

Against the wind, the airplane travels 1680 miles in 5 hours. So, the speed against the wind is : [tex]$ S_a = 1680 \div 5 = 336 $[/tex] mph

With the wind, the airplane travels the same distance of 1680 miles in 4 hours. So, the speed with the wind is: [tex]$ S_w = 1680 \div 4 = 420 $[/tex]mph

Let W be the speed of the wind.

Against the wind: [tex]$ S_a = S_w - W $[/tex]

[tex]\[ 336 = 420 - W \]\[ W = 420 - 336 = 84 \][/tex]

So, the speed of the wind is 84 mph.

Y varies jointly as x and z, and y = 32 m, x = 6 m, and z = 8 m. what is the value of y when x = 5 m and z = 12 m?
a. 90 m
b. 4 m
c. 40 m
d. 9 m

Answers

as x = 5 & z=12,

2/3 = y /(xz) = y/(5*12)

= y/60

so y / 60 = 2/3

y = (2*60)/3

= 40

Suppose a rectangular garden has a length of 3c + 15 feet and a width of 4c feet. write an expression for the area of the garden in square feet.

Answers

A = L * W

A = 4c(3c + 15)
A = 12c^2 + 60c <==

The area of the rectangle is given by the equation A = 12c² + 60c

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the equation will be

Let the length of the rectangle L = ( 3c + 15 ) feet

Let the width of the rectangle W = 4c feet

Now , the area of the rectangle A = length of the rectangle L x width of the rectangle W

Substituting the values in the equation , we get

Area of Rectangle A = ( 3c + 15 ) ( 4c )

On simplifying the equation , we get

Area of Rectangle A = ( 3c ) ( 4c ) + 15 ( 4c )

Area of Rectangle A = 12c² + 60c

Therefore , the value of A is 12c² + 60c

Hence , the area of the rectangle is A = 12c² + 60c

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ROUND 3.05947821031 TO THE NEAREST WHOLE NUMBER HELP

Answers

3 because the next number to the right is a 0 and will not be rounded up.

3.05947821031
^
whole number

if 3.xxx... < .5, round to 3.
If 3.xxx... > or = .5, round to 4.

Because .059 < .5, it is therefore rounded to 3.

The base of the parallelogram, b, can be found by dividing the area by the height. If the area of the parallelogram is represented by 6x2 + x + 3 and the height is 3x, which represents b, the length of the base

Answers

In this item, we have:

A = 6x² + x +3
h = 3x

where ''A'' is area and ''h'' is height. From the statement above,
length of base, b = A / h

b = (6x² + x + 3)/3x

Thus, the expression for the length of the base is 6x²+x+3 / 3x.

Answer:

[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]

Step-by-step explanation:

Given: The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.

To find: The base of the given parallelogram.

Solution: It is given that The area of the parallelogram is [tex]6x^2+x+3[/tex] and the height is 3x.

Now, area of parallelogram is given as:

[tex]A=b{\times}h[/tex] where b is the base and h is the height of teh gievn parallelogram.

Substituting the given values, we have

[tex]6x^2+x+3=b{\times}3x[/tex]

⇒[tex]\frac{6x^2+x+3}{3x}=Base[/tex]

⇒[tex]\frac{6x^2}{3x}+\frac{x}{3x}+\frac{3}{3x}=Base[/tex]

⇒[tex]2x+\frac{1}{3}+\frac{1}{x}=Base[/tex]

which is the required expression for the base of the given parallelogram.

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