Answers
Use the Law of Sines to find side b.
b / sin(B) = a / sin(A)
b / sin(59°) = 7 / sin(79°)
b = (sin(59°) x 7) / sin(79°)
b = 6.112
That is answer B.) 6.1 yards
Hope this helps!
Answer: Second Option is correct.
Step-by-step explanation:
Since we have given that
ΔSRT is a triangle with measures :
SR = 7 yd
∠T = 79°
∠R = 59°
We need to find the side ST say x.
We will use " Law of Sines " :
[tex]\frac{\sin T}{SR}=\frac{\sin R}{ST}\\\\\frac{\sin 79^\circ}{7}=\frac{\sin 59^\circ}{x}\\\\0.14=\frac{\sin 59^\circ}{x}\\\\x=\frac{\sin 59^\circ}{0.14}\\\\x=6.12\ yd[/tex]
Hence, the length of ST = 6.1 yd.
Therefore, Second Option is correct.
Related Questions
How do I solve this?
Answers
I find it convenient to draw a graph of a line that represents the ladder. I choose to have the y-intercept be where the ladder touches Catie's head (5.5 feet above the ground), and the x-intercept to be where the ladder touches the ground, 16 inches away from Catie.
Then the wall is 4.5 feet (54 inches) from the ladder's base, or 38 inches in the other direction from Catie. The graph shows the ladder hits the wall at a height of about 18.6 feet.
The graph shows the calculations for the position of the wall and for the equation of the line. (The line is written in "intercept form.") The graphing calculator shows the intercept points, so no "work" is required except to highlight them.
Jensen wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.75 square feet. The mirror is 4 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (2 points)
2x2 + 6x − 19.25 = 0
3x2 + 5x − 19.25 = 0
4x2 + 18x + 0.25 = 0
4x2 + 18x + 20 = 0
Answers
The frame will have the same thickness on both sides of the mirror. Therefore we add 5+x+x to get the total length, and we have 4+x+x to get the total width.
The area is found by multiplying the total width and total length:
A=(5+x+x)(4+x+x)
A=(5+2x)(4+2x)
Multiplying the binomials, we have:
A=5*4+5*2x+2x*4+2x*2x
A=20+10x+8x+4x²
A=20+18x+4x²
We know that the area is 19.75:
19.75=20+18x+4x²
We need quadratics set equal to 0, so subtract 19.75 from each side:
19.75-19.75 = 20+18x+4x²-19.75
0=0.25+18x+4x²
In standard form, it will be:
4x²+18x+0.25=0
Choose the polynomial that is written in standard form. (1 point)
−3x5y2 + 4x3y + 10x2
−8xy2 + 4x4y2 + 3x3
x4y2 + 4x3y5 + 10x4
x6y2 + 4x3y8 + 10x7
Answers
The only one where this is true is the first one.
The degree goes from 7 to 4 to 2
Answer:
[tex]-3x^5y^2+4x^3y+10x^2[/tex]
Step-by-step explanation:
A polynomial in two variables is in standard form if its monomial from left to right are arrangerd in descending order. We say that a monomial [tex]x^ay^b[/tex] is greater than a monomial [tex]x^{a^{\prime}}y^{b^{\prime}}[/tex] if [tex]a+b > a^{\prime} + b^{\prime}[/tex] or [tex]a+b=a^{\prime}+b^{\prime} \quad \text{and} \quad (a,b)>(a^{\prime},b^{\prime}})[/tex] in the alphabetical order.
For example
[tex]x^2y>xy \quad \text{since} \quad 2+1>1+1 \\\\x^2y>xy^2 \quad \text{since} \quad 2+1=1+2 \quad \text{and} \quad 2>1[/tex]
The polynomial [tex]-3x^5y^2+4x^3y+10x^2[/tex] is in standard form, since [tex]x^5y^2 > x^3y >x^2[/tex]. On the other hand, the polynomial [tex]-8xy^2+4x^4y^2+3x^3[/tex] is not in standard form since [tex]x^4y^2>xy^2.[/tex]
If it takes bottling machine to fill 150 bottles per minute, how many minutes will it take the machine to bottle 4500 bottles
Answers
How do I solve this? Please explain.
Answers
The first candle will have a volume of
.. V = Bh = (21 cm^2)*(8 cm) = 168 cm^3
The second candle will have a volume of
.. V = Bh = (7 cm^2)*(14 cm) = 98 cm^3
The total volume of the two candles is
.. 168 cm^3 +98 cm^3 = 266 cm^3
Josie is 6 cm^3 short of the amount required for the two candles she has in mind.
No, the base area of the second candle cannot be 7 cm^2. There is not enough wax to make a candle with that area 14 cm tall.
the sum of two fractions is three times their difference.six times the smaller fraction exceeds the larger fraction by 3/2.find the fractions
Answers
.. a +b = 3(b -a)
.. 6a -b = 3/2
Rewriting the first equation, we have
.. 4a -2b = 0
or
.. 2a -b = 0
Subtracting this from the second equation gives
.. 4a = 3/2
.. a = 3/8
.. b = 2a = 3/4
The two fractions are 3/8 and 3/4.
The width of Zorn’s patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?
Answers
4th option is the correct answer
Solution:
The shape of Zorn's Patio is rectangular, as shown in the given image/ The perimeter of rectangle is calculated as:
Perimeter = 2 (Length + Width)
Width is given to be = (7x+4) feet
Perimeter is given to be = (30x+26) feet
Using the formula of perimeter we can write:
30x+26 = 2(Length + 7x+4)
Taking out 2 common from left hand side, we get:
2(15x+13) = 2(Length + 7x + 4)
Cancelling the common 2 from both sides, we get:
15x + 13 = Length + 7x + 4
⇒
Length = 15x + 13 - 7x -4
Length = 8x + 9
Therefore, the length of Zorn's Patio is (8x+9) feet
Perimeter = (30x + 26)
Perimeter = 2( Length + Width)
30x + 26 = 2(Length + 7x + 4)
[Divide by 2 through]
15x + 13 = Length + 7x + 4
[Minus 7x on both sides]
15x + 13 - 7x = Length + 7x + 4 - 7x
8x + 3 = Length + 4
[Minus 4 on both sides]
8x + 13 - 4 = Length + 4 - 4
8x - 1 = Length
Length = 8x + 9 (Answer D)
Sandra can type 180 words in 3 minutes. At this rate, how many words can she type in 5 minutes?
_____MInutes
(FREE ANSWER> I WILL MARK BRAINLIEST AND RATE AND SAY THANKS)
Answers
60 x 5 = 300
she can type 300 words in 5 minutes
In your math class there are 15 boys and 21 girls. 12 of the boys and 15 of the girls are freshmen. if you randomly choose a student in your class, what is the probability that you'll choose a girl or a freshman?
Answers
Final answer:
The probability of randomly choosing a girl or a freshman from the class is 0.916 or 91.6%. This is calculated by considering the total number of girls and freshmen in the class, while avoiding double-counting freshman girls in the calculation.
Explanation:
To calculate the probability that a randomly chosen student from the class is either a girl or a freshman, we need to consider the total number of students in the class, as well as the number of girls and the number of freshmen. The class consists of 15 boys and 21 girls, totaling 36 students. Out of these, 12 boys are freshmen and 15 girls are freshmen, but we must avoid double-counting the girls who are also freshmen.
First, we calculate the total number of freshmen: 12 boys + 15 girls = 27 freshmen. Next, we calculate the probability of picking a girl: 21 girls / 36 total students = 0.583 (to three decimal places). We then calculate the probability of picking a freshman: 27 freshmen / 36 total students = 0.750. However, since the freshmen include both boys and girls, we must subtract the probability of picking a freshman girl to avoid double-counting: 15 girls who are freshmen / 36 total students = 0.417.
Finally, we add the probability of picking a girl and the probability of picking a freshman, and subtract the probability of picking a freshman girl to obtain the inclusive probability: 0.583 (girl) + 0.750 (freshman) - 0.417 (freshman girl) = 0.916.
Therefore, the probability that a randomly chosen student is either a girl or a freshman is 0.916, or 91.6%.
At 9:00 am two cars started from the same town and traveled north on the same road. one ca traveled at a rate of 35 mph and the other at a rate of 40 mph. after how many hours will the cars be 30 miles apart
Answers
40 x 6 = 240
240 - 210 = 30
so after 6 hours the cars will be 30 miles apart
A jar made of 3/16-inch-thick glass has an inside radius of 3.00 inches and a total height of 6.00 inches (including the bottom thickness of glass). The glass has a density of 165 lb/ft3. The jar is placed in water with a density of 62.5 lb/ft3.
Assume the jar sits upright in the water without tipping over. How far will the empty jar sink into the water?
What is the volume of the glass shell of the jar? Precision 0.00
What is the weight of the jar? Precision 0.00
What is the weight of water the empty jar will displace? Precision 0.00
What is the volume of water the empty jar will displace? Precision 0.00
How far will the empty jar sink?
Answers
The total volume of the jar is:
[tex]V_t=Bh=\pi h(r+a)^2[/tex]
Where h is the height of the jar, a is the thickness and r is the inner radius.
The volume of empty space, bounded by the jar, is:
[tex]V_e=B(h-a)=\pi r^2(h-a)[/tex]
The volume of a jar shell is the difference between these two:
[tex]V_s=V_t-V_e=\pi h(r+a)^2-\pi r^2(h-a)[/tex]
When we plug in all the number we get:
[tex]V_s=27.17 {$in}^3[/tex]
The weight of the jar is simply its volume times its density. We have to convert density of the glass:
[tex]165 \frac{lb}{ft^3}=\frac{165}{1728}\frac{lb}{in^3}=0.0949\frac{lb}{in^3}[/tex]
Now we can find the mass:
[tex]m_j=V_s\rho_j=27.17\cdot 0.0949=2.58 $lb[/tex]
The volume of water jar would displace depends how far the jar would sink.
There two forces acting on the jar when you put in the water. The first one is gravity and it's pulling the jar down. The second force is the buoyancy the and this force pushes the jar upward. In order for that jar to be stable, these two forces must be the same.
The buoyancy is given with this formula:
[tex]B=\rho gV_{disp}[/tex]
The volume of water that would be displaced by the jar can be expressed by this formula:
[tex]V_{disp}=\pi h'(r+a)^2[/tex]
Where h' is the height of the jar that is submerged in the water.
So the buoyancy force is:
[tex]B=\rho_w g\pi h'(r+a)^2[/tex]
This force must be equal to the force of gravity acting on the jar:
[tex]F_g=B\\ m_jg=\rho_w g\pi h'(r+a)^2\\ m_j=\rho_w \pi h'(r+a)^2\\[/tex]
We solve for h':
[tex] h'=\frac{m_j}{\rho_w \pi(r+a)^2}[/tex]
If we plug in the number we get:
[tex]h'=2.24 $in[/tex]
Now we can calcuate the amount of water discplaced and its mas(keep in mind that we also converted density of water into lb/in^3):
[tex]V_{disp}=\pi h'(r+a)^2=71.50${in}^3\\ m_v=\rho_w\cdot V_{disp}=2.58$lb[/tex]
We get the same mass as the mass of the jar, which makes perfect sense:
[tex]m_jg=\rho_w V_{disp}g\\ m_j=m_{wdisp}[/tex]
The volume of the glass shell of the jar is 0.0136 ft³ and its weight is 2.24 lbs. The weight and volume of the water it will displace amounts to 2.24 lbs and 0.036 ft³ respectively. Consequently, the jar will sink approximately 2.2 inches into the water.
Explanation:To begin, the volume of the glass shell of the jar will first need to be established. Given that the thickness of the glass is 3/16 inches, the outer radius of the jar is 3 inches + 3/16 inches = 3.1875 inches. To get the volume, utilise the formula for the volume of a cylinder, which is πr²h. Thus, with measurements converted to feet for the calculations (1 inch = 0.08333 foot), we have an external volume of π(0.265625 ft)² * 0.5 ft = 0.1118 ft³ and an internal volume of π(0.25 ft)² * 0.5 ft = 0.0982 ft³. Hence, the volume of glass is 0.1118 ft³ - 0.0982 ft³ = 0.0136 ft³
Next, the weight of the jar is determined by the formula mass = volume * density, so mass = 0.0136 ft³ * 165 lb/ft³ = 2.24 lbs.
To ascertain the weight of water the jar will displace, we consider the principle of buoyancy, which suggests that an object will displace a volume of fluid with a weight equal to its own weight. Thus, the weight of the water displaced is 2.24 lbs.
Then, the volume of this water is found with the formula volume = weight/density -> volume = 2.24 lbs / 62.5 lb/ft³ = 0.036 ft³.
Lastly, considering the jar will sink until the weight of the water being moved equals the weight of the jar. The volume of the water displaced equates to the submerged volume of the jar. Its depth in feet is then the volume divided by the cross-sectional area of the jar (internal radius), so the distance the jar sinks is roughly 0.036 ft³ / π(0.25 ft)² = 0.18 ft -> convert to inches = 2.2 inches.
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What equation results from completing the square and then factoring x^2-12x=58
Answers
The correct answer is (x - 6)2 = 94
Answer:
A for me
Step-by-step explanation:
Molly can either take her lunch or buy it at school. It cost $1.95 to buy lunch. If she wants to spend no more than $30 each month, how many lunches can she buy at most?
Answers
Final answer:
Molly can purchase a maximum of 15 school lunches per month with a budget of $30, considering each lunch costs $1.95.
Explanation:
The question asks how many school lunches Molly can buy if each lunch costs $1.95 and she wants to spend no more than $30 each month. To find out how many lunches Molly can buy, we divide her monthly budget by the cost of one lunch.
So, we perform the calculation: $30 ÷ $1.95 ≈ 15.38. Since Molly cannot buy a fraction of a lunch, we round down to the nearest whole number, which means Molly can buy 15 lunches at most in a month without exceeding her budget.
Matt is saving to buy a new motorcycle. If he deposits $60 at the end of each month in an account that pays an annual interest rate of 3.5%, how much will he have in 15 months? Assume that the compounding is being done monthly.,
Answers
You need to apply the following formula:
C = P[ [tex] (1+r)^{t} [/tex] - 1]
where:
C = compound interest you need
P = original amount of money deposited
r = is the rate, written as a rational number
t = number of months
Pluggin in numbers:
C = 60[ [tex] (1+0.035)^{15} [/tex] - 1] = 40.52$
Now, you need to add this amunt to the original amunt:
(60+40.52) = 100.52$
Therefore, Matt will have 100.52$ after 15 months.
PLEASE HELP ME ASAP
PLEASE
Answers
Choice D
Company 2 is greater in avg rate of change by $750
=======================================
Explanation:
Average rate of change is the same as slope through two points. The two points are the endpoints of the interval.
The x values we'll use is x = 0 and x = 12 since it constitutes the first 12 years (12-0 = 12)
For company 1, if x = 0 and x = 12, then y = 12000 and y = 30000 respectively. The two points (0,12000) and (12,30000) are on the graph for company 1
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (30000-12000)/(12-0)
m = 18000/12
m = 1500
Over the first twelve years, the average rate of change for company 1 is 1500
For company 2, the points (0,15000) and (12,42000) are on the graph
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (42000-15000)/(12-0)
m = (27000)/(12)
m = 2250
Over the first twelve years, the average rate of change for company 2 is 2250
Now find the difference in the slopes
2250-1500 = 750
Company 2's rate of change is larger by $750
So that's why the answer is choice D. Over this timespan, company 2 is growing faster on average compared to company 1
Convert 4 miles to feet.
20,210 feet
21,000 feet
21,120 feet
22,000 feet
Answers
Can someone explain the Pythagorean theorem to me, please?
Answers
Pythagorean theorem is a²+b²=c².
a is the length is the leg, b is also a leg and c is the hypotenuse
***WILL GIVE MEDAL TO WHOEVER HELPS***
Question:
Sherri has 23 pieces of jewelry to sell. She sells the bracelets for $2 and the necklaces for $3, and earns a total of $55. If the bracelets are represented by x and the necklaces are represented by y, which of the following systems of equations can be used to calculate the number of bracelets and necklaces sold?
Answer choices:
x + y = 23, 3x + 2y = 55
x + y = 55, 3x + 2y = 23
x + y = 23, 2x + 3y = 55
x + y = 55, 2x + 3y = 23,
Answers
#16 ) BRAINLIEST + POINTS !!!!!
Answers
Answer:
b is correct
Step-by-step explanation:
10 POINTS + BRAINLIEST ANSWER!!
Let the function f be defined by f(x) = (x - 1)(x + 7). Which of the following is an equivalent form of f in which the minimum value of f appears as either a coefficient or a constant?
A. f(x) = x^2 - 7
B. f(x) = x^2 + 6x - 7
C. f(x) = (x + 3)^2 - 16
D. f(x) = (x - 3)^2 - 20
Answers
All you have to do is foil
How do you find the x intercept, y intercept, and M
Answers
.. (2x/12) + (-3y)/12) = 1
.. x/6 + y/-4 = 1
The x-intercept is 6
The y-intercept is -4
The "slope triangle" is 4 units high and 6 units wide, so ...
.. the slope is m = 4/6 = 2/3.
Taylor is competing in a 30 km race. She has already run 12.35 km through a park and swam 3.75 km. She will bike the rest of the way. Round each distance to the nearest km. About how far does Taylor need to bike to finish the race? A. about 12 km B. about 13 km C. about 14 km D. about 23 km
Answers
12km + 4km = 16km
30km - 16km = 14km
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
V(t)=24,500(0.95^t)
Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.
Answers
The value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
The dollar value v(t) of a certain car model that is t years old is given by the exponential function.
[tex]\rm V(t)=24,500(0.95^t)[/tex]
The initial value plug t = 0 in the above function:
V(0) = $24500
Plug t = 13 years in the above exponential function
[tex]\rm V(13)=24,500(0.95^1^3)[/tex]
After calculating, we get:
V(13) = 12576.88
V(13) = 12576.9 dollars
Thus, the value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
Learn more about the exponential function here:
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If x and y are positive integers, what is the value of x + y ? x+y=15 xy=6
Answers
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
Answers
then y+(x+2)+(x-2)+(x-10) = y +3x -10 =360 (by adding both sides by 10)
y + 3x =370 ;.... eq 1
the sum of each two opposite sides in a quad inscribed in a circle =180
then (x+2)+(x-2)=180
therefore 2x =180
therefore x=90 (sub in eq 1)
y+3*90 =y +270 = 370 (subtracting both sides by 270)
therefore y=100
then measure angle B=100 degrees
A=92 degrees
C=88 degrees
D=80 degrees
The following is an idealized equation representing the world population of Leatherback turtles, where t represents time in years since 1970.
f(t) = 50,000(.92)^t
How would you determine the population in the year 2000?
Is this a growth or a decay function?
How can you tell a growth or decay function just by looking at it?
Answers
so population in 2000 = 50,000 * (0.92)^30 = 4098 Asawer
This is a function of decay.
The function is decay because the number in the parentheses is < 1.
On a rombus AB=27, m
Answers
Please help me asap!!!
Answers
-x - 2y = - 9
multiply the (1st) equation by 3
-3x - 6y = -27
now you have
-3x - 6y = -27
3x - 6y = -15
-----------------------add
-12y = -42
y = 3.5
2(3.5) = -x + 9
7 = - x + 9
x = 2
answer
(2 , 3.5)
am i correct?
Which of the following describes how to translate the graph of y = |x| to obtain the graph of y = |x + 1| - 2?
shift right 1 and down 2
shift left 1 and down 2 <<<
shift right 1 and up 2,
Answers
Answer: both of u are wrong its one unit shift up one unit shift down
Please help asap!!! 16 points ):
Answers
ANSWER: D) x=3
Hope this helps! :)